How do you get silver account on Xbox?

You are automatically a silver account when registering for Xbox Live. This can be done one of two ways:

Either you can join Xbox Live online through this website

http://www.xbox.com/en-US/live/joinlive.htm

or

You can setup a Live account directly from your Xbox 360. If you already registered an account through the website, you should be able to enter the login information through the Xbox.

No credit card information should immediately be needed as well, unless you're upgrading to a gold account.