There are 4 ways to get Bitcoin.
1. Buy it by converting an existing FIAT currency for it.
2. Be a Merchant that accepts it for goods or services.
3. Mine it
4. Receive it as a gift

Regardless of the method of obtaining it, Bitcoin is sent to a public address that you own the private key for.

How do I buy Bitcoin?

What Exchanges are good to use?

How do I get Bitcoin as a gift?

Mining is the process by which the unconfirmed transactions become confirmed.
You mine bitcoin by either installing the bitcoin-qt software or joining a mining pool and then running a mining software (like cgminer) that uses your CPU/GPU/ASIC cards to solve hashes.
What you are looking for with this software, is the Nonce that is used to provide the proof-of-work for the block that confirms the block as valid.
Mining uses difficulty, to scale the network so that on average, there is a block found every 10 minutes. See (Mining Difficulty)

You can see who has mined each block, by viewing the Hashrate Distribution chart.

What is Mining, specifically?

You receive bitcoin, using your public address. This address will look something like this: 18dAhXSeeazgVSmYF78o4z34Z9XUpN7Njj
People send bitcoin to this public address, and once confirmed, the coins are then associated with this address and not with their previous address.

QR Codes are widely used to contain the public address instead of typing the long string above.

Using your wallet software. You send coins that you control (own the private key to), to any public address.
You cannot send anything without the private key. And you cannot send anything you do not have. In this way, it is not possible for someone else to send your coins, or for you to send coins you do not posesses.
The private key is NEVER given out publicly to the network, even when sending coins. What is sent, is a signature that can only be created using the public/private keys. See Bitcoin Transactions.

Vendors will and are arising to accomplish this task for you as well, as easily as possible. One company gives you a debit card, which you can use at any of their POS termials. This is Coinkite.

You can sell Bitcoin in the same way that you buy it. Through an Exchange (Such as Bitstamp, Gemini, Poloniex, etc), through a payment processor (BitPay, etc), or locally to another person (LocalBitcoins).

Typically, if you want to convert back to FIAT you would use a merchant account system. These systems use callbacks so you can tie order information to the data sent to the site and track who orders what.
An example of this is Bitpay. These services typically come with a 1% or flat per-month fee to auto-convert bitcoin to FIAT currency.

Of course, you can accept payment directly in bitcoin yourself with no 3rd party required - using your own wallet.

On July 30, 2014 - BitPay changed to a $0 / 0% forever policy. So it costs nothing to accept and convert bitcoin for your business.

Look at your credit card processing fees. Chances are, you are paying at least 4% on every transaction. Using services from Bitpay, you would only be paying 1% (or fixed per month) if you chose to convert Bitcoin transactions to FIAT currency. If you keep your payment in Bitcoin, there is usually little to no fees. This is a HUGE savings and is the single greatest reason a Merchant should look into accepting Bitcoin.

A wallet, is just a collection of public keys (addresses) that are derived from the private key(s) in the wallet. The wallet also contains the private key associated with the change address(s).

Types of Wallets

Where can I get a wallet?

As with any free market, price goes up and down based on supply/demand. That means, that at any given time, the conversion rate of BTC to any FIAT currency will change.
If you enjoy volatility as a trader, this is a good thing, as the market goes up/down, you can buy/sell to turn a profit.
As a merchant, you may not want to deal with the volatility of the price. So you simply price your product in whatever FIAT currency you wish, the buyer sees that price auto-converted to BTC, you take the BTC as payment and it's automatically converted back to FIAT for you. (see the 3rd party payment systems for this method).
The point is, you can worry about volatility, or not. It is entirely up to you. But volatility in a free market, is a totally normal thing.

Either Bitcoin will fail, or it will succeed, there is no middle ground - "logarithmic, hold onto your hats, this is going to be a wild ride"

It can be. Speak with your financial advisor on if this is a long term investment for you or not. (assuming your Financial Advisor knows anything about Bitcoin) The general consensus is "do not invest more than you are willing to lose" - this is true for any investment - be it bitcoin, or stocks, or anything else.

There are a few, personally I like: Bitcoin Average.

However, if you want to see prices in Satoshi, use the site you are on now.
A good graph based site is: Bitcoinity
Another great graph based site with alarms and many alt-coins is: BitcoinWisdom

A great Android app to check price (and get alerts) is Bitcoin Checker.

To me, the only price that matters currently (until FIAT is no longer needed), is what I can get if I want to buy/sell a bitcoin for FIAT (USD). So for me, Gemini is the only price that matters.

There will be a total of 21,000,000 Bitcoin by the year 2140. The "reward" for each solved block started at 50 coins awarded, and is halved about every 4 years (210,000 blocks). See: Controlled Currency Supply.
However, Bitcoin is expressed with 8 digits past the decimal place. Ex: 1 BTC = 1.00000000 BTC and so the actual usable units of value is 100,000,000 * 21,000,000 = 2,100,000,000,000,000 units of value. This number can be increased as needed with simple code changes.

Actually, your credit card doesn't confirm funds for up to 120 days after you discover a problem - or 540 days after the transaction (see Credit Card Chargeback rules). Within those 120 days, the funds can be reversed by the payee/financial institution and the merchant can not get that money.
What happens instantly, is that upon attempting to spend money on your credit card, a verification is done that checks that your available balance will allow the transaction at that moment.

Bitcoin does this at the core of the system. You can not spend coins you do not own (balance > what you are attempting to spend) and if someone was attempting to double-spend, it would need to occur at almost the same moment - so within seconds, you can be very certain there is no double-spend occuring.
The coins are then verified within approximately 10 minutes, and CAN NOT be reversed after those 10 minutes. - Compared to Credit Cards where a transaction can be reversed up to 540 days later.

Typically, as long as the recommended mining fee is included in the transaction, it can be assumed that the transaction *should* get into a block. As of Feb 2014, plans are in place for a payment protocol change to allow a better guarentee that the mining fee is included in the transaction.

Bitcoins get included in transactions on a priority basis by the miners. (see: Transaction Fees).
If you do not include a mining fee on your transaction, it could take weeks or months before the miners actually include the transaction. So by including a small (as of 1/6/14 this is about .0001 btc) amount in the mining fee, will guarentee the transaction to get into one of the next 1-2 blocks.
The mining fee is paid for by the SENDER of the coins. Not the receiver.
Say for example, you want to send 0.1 coins from X to Y. If you only have 0.1 coins in your wallet, you would not be able to send that amount. As you would only be able to send 0.0999 coins, since you need to include the recommended mining fee of .0001 (as of 1/6/2014)

All transactions contain inputs and outputs. Since there is no guarentee that the sum of the inputs will match the outputs, change must be given. Change is simply, the remainder of the inputs-outputs which is sent to an address. See Change.

Under the current model of encryption (RIPE-MD160) there are approximately 2^120 addresses - or 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976 possible addresses. For perspective, the total number of grains of sand on the planet earth is only 2^63 estimated.

An Alt-Coin is simply another coin that has been created using the Bitcoin Protocol as a basis.

As of December 2013, there are about 110 different Alt-coins but this number continues to grow. You can trade them at exchanges such as: Poloniex.

Sites like CoinmarketCap exist to list out every coin and where you can trade them at.
Early notable coins are/were:
Litecoin
Peercoin
Namecoin
Dogecoin
In 2014, there was a big push to be more anonymous. New coins sprung up to solve this problem, some notable ones are:
DarkCoin (rebranded to Dash)
Monero

Coins also appear that are industry specific. In June 2016, TitCoin was created.

Coins also appeared to work as contracts. Ethereum was the first to do this but many others have also attempted it.
Coins have appeared to store files (like dropbox) - Storj and Siacoin are examples of this.
Coins appear that use totally different (or new) methods - such as a DAG coin like IOTA which uses what they call the "tangle" which is the blockchain - except as a web instead of a chain.
Since "alt-coins" are simple to create - almost anybody can create them. That also means, they can live and die very quickly. Typically, once listed on an exchange, an alt-coin will live and die by the price that the market gives to it. If there is little to no trading volume, the coin will be delisted, which usually marks its death. If the coin trades well, and developers keep active, the coin can continue on for quite a while. It's certainly possible in the future, that an "alt-coin" replaces Bitcoin as the most widely used coin.

2FA or Two-Step Authentication is setting up a logon to something to use Two methods of authentication.

For example, a password AND a code that is sent to an SMS number or e-mail address.
Or a password AND a code that is provided by an application running on a phone.

The most basic method, is an SMS code sent via Text-Message to your phone number upon attempting to log on.
Google Authenticator is an application maintained by Google which also does this for you.
However - I like to use a program like: Authenticator Plus over google wallet because you can backup the keys and re-import them (if you change your phone out).

2FA is HIGHLY recommended on any website that you store anything of value on. It should protect against people being able to log into a website by simply knowing your username and password.

An exchange is simply a website that "exchanges" bitcoin for something else. For example, exchange bitcoin for litecoin or dogecoin or FIAT currency.

It should be noted, and STRESSED that an exchange is a 3rd-party. *ANY* funds you move to an exchange are *NOT* controlled by the bitcoin network and are solely controlled by the exchange. (as of Mar 2014).
What this means, is that an exchange can and has closed/been hacked/stolen customer funds, and currently, there isn't anything you can do about it.
The most notable, happened in February 2014 when one of the first and biggest exchanges (Mt. Gox) stopped all trading and declared bankruptcy. Other exchanges have closed or been hacked.

DO NOT store funds on an exchange that you are not willing to lose, and DO NOT use an exchange in place of your own wallet.

Some examples of an exchange are: Bitstamp, Poloniex, BTC-E, Bitfinex, Kraken, Bittrex etc.
Sites like CoinmarketCap exist to list out every coin and which exchange you can trade them at.

If you do not want to use an exchange, sites such as Shapeshift have appeared which will convert between different coins for you without an account. (you just need a wallet address for each coin).

Increasingly, more and more locations are accepting bitcoin as a form of payment.

There are a few websites dedicated to tracking these sites, for example: Spendbitcoins, or Coinmap.
Also, the Bitpay Merchant List is a good starting points for vendors who convert bitcoin to FIAT upon purchase.

Some of the major retailers that started accepting bitcoin, are:
Overstock.com - Added January 2014
Tigerdirect.com - Added January 2014
Expedia.com - Added June 2014
NewEgg.com - Added July 2014
Dell.com - Added July 2014

Currently (March 2014) the answer is yes, and no.

First - take a look at what fungibility is over at Wikipedia. One bitcoin currently has the same value as another, there is no difference.
However - the origins of a bitcoin can be tracked all the way back to when it was added to the network as a block reward. Bitcoin is not (yet) truely anonymous. (see Anonymity). So it is possible for a bitcoin to - in the future - NOT be fungible. This would not be a good thing, as fungibility is a requirement of a currency system.

There are (as of March 2014) some proposed changes to make sure that Bitcoin is truely anonymous and fungible, one of these is: Zerocoin.