Bitcoins are an Internet based currency and therefore is a digital thing and you will need a Bitcoin wallet to hold your Bitcoins. Wallet.dat
To get started you will need to go to the Bitcoin web site and download the Bitcoin client.
Make sure that you get the one for your operating system and once it's downloaded you can open it and it will start to download the blockchain. The blockchain is where you get the Bitcoins and resolving parts of the blockchain produces Bitcoins.. Once the blockchain is downloaded, and it can take a while, and updated you need to click on New to get your Wallet.dat address. This address is a long series of numbers and letters so it should be written down and kept someplace safe, maybe even store a copy on a USB stick.
As a matter of convenience you should order a copy of the blockchain on DVD so you will have it and not have to keep downloading it it's lost in a computer crash or is accidently deleted.
You need to download the bitcoin client and get you wallet and order your blockchain DVD. Download the blockchain and secure your wallet.dat which can be done by following the instructions on this web page.
You need a mining computer or you need your computer to be able to mine bitcoins. One of the better ways is with a GPU miner. A GPU miner is a computer that has an AMD card or several AMD cards in it as AMD video cards provide a better result since they are good with algorithms and will perform better then Nvidia cards.
You will need to join a pool since mining by yourself is frustrating and will yield little or no results. Joining a pool will allow you to become part of a group and the combined processing power will yield more bitcoins and they will be shared amongst the group according to each members contribution. Any bitcoins that you earn should be stored in a safe place to prevent accidental deletion from a computer crash or loss of power. Once bitcoins are lost they are lost for ever and cannot be retrieved.
Before investing any money in special equipment you should start out with what you have and see what can be gained. Since AMD video cards will provide a better mining operation if you already have one then you will be in good shape to get started and see what it will produce. Then you can decide if you want to add another card or set up a specialized computer that will run 24/7 to produce bitcoins. This link will show you the best hardware for mining and compare the different components. Also it will give you a breakdown of the different mining computers for sale.
Electricity! The cost of running a computer 24/7 or for long periods of time have to be factored into the overall cost so if the cost of electricity is high where you live you may want to consider if it's worth running a bitcoin mining macine. To produce anything worth while the miner should be running 24/7.