How Do I Signup for Adsense ?

If you have your own website already, jut go to the Google Adsense site and sign up.
If you are going to start with a blog on Blogspot , then just start your blog there. Once you have done the initial setup there you can click on the Layout tab and choose to "Add a Gadget" then select the button for Adsense. If you don't have an account you will be prompted to set one up. What could be easier??

Do I Need to Buy a Website ?

No!
You will need a website or a blog to use adsense. You can use the adwords program (part of Adsense) without any website at all - but that involves paying for clicks, is quite involved and carries some financial risk. The easiest, and by far the cheapest, way to get started is with a free blog on Blogspot , now owned by Google.

Anyone can make money with Adsense

Of course, you've probably seen all the hype about making money on the internet. Making money with Adsense is part of that hype, but it is also quite true. Anyone really can make money on the internet with Adsense.
For the average person, the issue is not whether or not you can make money this way - but just how much money you can actually make in a given period of time. Don't fall for those $3,000 a month-quit-your-job-now schemes that you have to pay good money for. It really is free to get started, so don't pay anyone a dime!