Is it possible for website owners to find out what other websites we visit? If so, how do they find out? Thanks

One word: cookies

Does that mean I should delete my cookies immediately after coming here so that the other website cannot find out I came here?

Or if I use a different browser for each website?

Opening a different browser window with the same browser would not work. I'm not sure if using a completely different browser like Firefox or Opera would work.

Not all cookies can be read by other places. Not all cookies are bad. But some are not very nice. But it certainly doesn't hurt to delete your cookies when you get done browsing. Also, spyware programs can find the bad ones and delete them for you. You can also turn up the cookie setting in IE, under Tools --> Internet Options --> Privacy. Do keep in mind this might keep you from doing certain things.

If you don't want to be tracked I suggest this download

Go-Liberty Free Download - Surf the Internet, download, chat without being tracked and keep your privacy.

how to keep from being tracked on internet - Google Search

Hope this helps -- Please rate my answer

Cookies have gotten a much maligned reputation. Essentially a cookie is a small text file, often encrypted, that some WEB sites leave on your PC to identify you when you return. The purposes is to customize the site to you individually. But cookies can be used maliciously. Also advertising sites like doubleclick.com use them to track your interests, again to customize the WEB for you. Most of this is done without capturing or storing anyting that is traceable to you. For example, if you bought books from a specific author at one book site, you might find that author being presented to you at another site. But that's done dynamically so the site doesn't store you preferences on their machines.

Why are you concerned about this?