What are the rules for creating a fansite on let's say my favorite tv show?

That all depends on the copyright rules and terms of use for each individual asset. For example the terms of a movie trailer my specify that you are allowed (and actually encouraged) to share it. On the other hand, a picture taken from Google Search may not be OK to display because the owner of that picture has different copyright terms that don't allow you to use the image without consent.

In general, you can use something if you made it, bought it or have permission to use it. It's also best practice to credit the source, and also to link to the source when you use something that's not yours.

compfight.com freeimages.com istockphoto.com

here is a list of some sites that you can use to search for some images that you can use on a site like you described to help narrow your search for free to use images look under the creative commons license tabs for example on compfight.com it is in the left hand nav area after you complete a search ..