Most of info sourced from bitcoin.org
Bitcoin is one of the first implementations of a concept called crypto-currency, which was first described in 1998 by Wei Dai on the cypherpunks mailing list. Building upon the notion that money is any object, or any sort of record, accepted as payment for goods and services and repayment of debts in a given country or socio-economic context, Bitcoin is designed around the idea of a new form of money that uses cryptography to control its creation and transactions, rather than relying on central authorities.
In 2009, the first Bitcoin specification and proof of concept was published in a cryptography mailing list by a member under the pseudonym of Satoshi Nakamoto. Towards the end of 2010 Satoshi left the project, saying he had moved on to other things. The creator of Bitcoin never revealed his identity and simply left his invention to the world. The origin and the motivation behind Bitcoin are still today a great source of mystery.
Since 2010, the Bitcoin community has grown with many developers working on the project. During June and July 2011, Bitcoin suddenly gained media attention leading to a massive buy rally. The resulting bubble slowly deflated through the latter part of 2011, and since then the value of Bitcoin has slowly climbed once again back to its 2011 heights.
On September 27th 2012, the Bitcoin Foundation was created in an effort to standardize, protect, and promote Bitcoin. Today, the Bitcoin economy is developing quickly with new users joining every day.
BitCoin what are they?
To put it simply it is a online currency. 1 BitCoin is worth around 105 USD
BitCoin are they legal?
Yes and No. If you are in a pool it is Fully LEGAL as they should pay the tax and if they don't they get shut down and you get your coins. If you do it alone you must pay the tax.
BitCoins How do i get them?
There are two methods. Buy them using your local currency e.g USD or GBP
You can mine them with any good PC
DON'T CPU MINE you will loose you need to GPU Mine with your GFX card.
Now, i am going to tell you how to join a pool to mine not our self.
•First find a Pool you like the sound of (see below for the different types).
•The go to http://bitcoin.org and watch the video if you want then press get started with bitcoin.
•Choose your wallet (MultiBit) download it.
•The register with your chosen pool.
•They will give you a worker ID and password. Go to http://guiminer.org/ and download it.
•Put the username/worker id in the box and same with password.
•Then start Mining
BitCoins Types of Pools
Types of Pools.
DGM - Double Geometric Method. A hybrid between PPLNS and Geometric reward types that enables to operator to absorb some of the variance risk. Operator receives portion of payout on short rounds and returns it on longer rounds to normalize payments. 
Prop. - Proportional. When block is found, the reward is distributed among all workers proportionally to how much shares each of them has found.
PPLNS - Pay Per Last N Shasres. Similar to proportional, but instead of looking at the number of shares in the round, instead looks at the last N shares, regardless of round boundaries.
PPS - Pay Per Share. Each submitted share is worth certain amount of BC. Since finding a block requires <current difficulty> shares on average, a PPS method with 0% fee would be 25 BTC divided by <current difficulty>. It is risky for pool operators, hence the fee is highest.
SMPPS - Shared Maximum Pay Per Share. Like Pay Per Share, but never pays more than the pool earns. 
ESMPPS - Equalized Shared Maximum Pay Per Share. Like SMPPS, but equalizes payments fairly among all those who are owed. 
RSMPPS - Recent Shared Maximum Pay Per Share. Like SMPPS, but system aims to prioritize the most recent miners first. 
CPPSRB - Capped Pay Per Share with Recent Backpay. 
POT - Pay On Target. A high variance PPS variant that pays on the difficulty of work retuened to pool rather than the difficulty of work served by pool 
Score - Score based system: a proportional reward, but weighed by time submitted. Each submitted share is worth more in the function of time t since start of current round. For each share score is updated by: score += exp(t/C). This makes later shares worth much more than earlier shares, thus the miner's score quickly diminishes when they stop mining on the pool. Rewards are calculated proportionally to scores (and not to shares). (at slush's pool C=300 seconds, and every hour scores are normalized)
to choose a pool for you https://en.bitcoin.it I use mining.bitcoin.cz Becuase it is fair