Here's the official installation guide:-
Are you planning to run Magento in your own computer? If so you need to get all the necessary software setup and ready in your computer before you can proceed.
Magento is meant to run from a server and not in a computer so it's not a Windows software where you can install with a setup .exe file.
You can install and run it in your computer but before you do, you will need to setup all the necessary software like Apache, PHP and MySQL in your computer first (which is normally by setting up Xamp or Wamp).
Ask yourself these questions?
Do you plan on accepting credit cards? If so than you will need to be PCI complaint. I would recommend a VPS server or a fully maintained server that you control. However, if you know nothing about handling a server than you will need a fully dedicated server but those are expensive.
I had this problem. I had to become PCI compliant and the server I was on isn't compliant, so I switched to my own VPS server.
A decent VPS server could be like $4.99 a month; Dedicated Server maintained can be very costly like $100 a month or more. Personally if you want to run your own server either go with Linux or pay for a VPS. Than do a PCI Scan which there is a free one Trial and Hackerguardian.com. It will show you vulnerabilities in your server that you need to fix. Most servers now use SuExec which makes files and folders more secure by not allowing permission to go over a certain limit. Running a server isn't that hard once you know the basics like permissions, Ip Filtering, etc
@drillsar12: There are some modern payment processors like Stripe and Braintree which will ensure that the card data is not passed through your server so the PCI burden is greatly reduced.
What you are suggesting (managing his own VPS) is way over the OP's head if he has problem even with Magento installation so I wouldn't recommend that he go with that route. Managing a server properly is a complex and time consuming process which is not for everyone.
Anyway we are veering off-topic as that's not what the OP is asking about. Let's keep things on topic please.