There are two ways to get bit coins. You either buy them or you mine them.
www.tradehill.com (TH-R12733 for 10% discount on fees)
www.mtgox.com
Are the two more popular sites currently to buy and sell Bitcoin (BTC).
Get the Bitcoin client from www.bitcoin.org
Install
This will ideally run all the time.
Opening port 8883 will vastly increase the block communication.
Next we need a miner. There are plenty, I'm using GUIMiner.
Head over to this thread http://forum.bitcoin.org/index.php?topic=3878.0 - Download and install the latest build.
Pick a mining pool. Mining pools vary a lot on fees and what they offer. It doesn't ultimately matter if you go with a popular or lower populated pool. In the end you earn the same amount of BTC sans fees.
The only difference is how often a block is found and the reward is split.
Fast pool = more people to split with = steady earning rate
Slower pool = less people = bigger splits = slower earning rate
As long as the pool you join is earning in the Ghash/s range, you will have a fairly steady rate of coin.
Mining Pools
www.btcguild.com
www.bitcoins.lc
www.bitcoinpool.org
There are many other pools to choose from at http://forum.bitcoin.org/index.php?board=41.0
A pool that is overloaded is prone to downtime which means you earn nothing if you are away, sleeping, whatever. Make sure to setup a backup pool as well.
Pool Worker
You need to make a worker for your specific pool. Whichever pool you join will have a way for you to create one.
Typically it will be: username.workername or username_workername (note the underscore or period) and password set for the worker.
Most pools have a FAQ on how to connect, use workers, read it if you are unclear. This should get you on your way to mining BTC.
Optional Reading Below
GPU vs CPU mining
At this point in the game, you must use a GPU (AMD ideally) that supports OpenCL (AMD 4xxx and up). CPU mining is not profitable anymore. A $100 GPU can hash out faster than your $1000 CPU tenfold.
nVidia GPU's are not good at all for mining compared to AMD.
https://en.bitcoin.it/wiki/Mining_hardware_comparisonBlocks and Shares
When a block is solved, 50 BTC are awarded. When you are joining a pool, you are with a team to solve that block and get the 50 BTC bounty which will then get split. If you decide not to join a pool and go solo, it can take you months to solve that block. It is a lottery ultimately and you could solve it in 10 minutes or 10 months