I am trying to build a website, and am wondering if I browse around the internet (like Google images or somewhere) and find little icons or little pictures, which ones can I use on my site? How can you check if they are copyrighted or not?

You'd check the website to see if its design is copyrighted.

For a couple of free ones, you could try:

http://www.webdesign.org/web/free-stuff/icons/

Go to google and type in royalty free images. These are images that you are allowed to use.

Royalty free (http://en.wikipedia.org/wiki/Royalty_free) doesn't necessarily mean free to use, that usually just means they can be used without paying additional fees beyond the initial cost.