copyright - How do I know which images are copyrighted and not?

Using google images you can find any image you want these days, even high resolution. The question is how do I know what I can use image wise in the graphic design work assuming that the graphic work is for non profit use?

For example, I want to use Garfield comic strip, a portrait of Mark Twain, a book cover of some novel. Are any of these things restricted or can I use them without seeking permissions? And do I have to even seek for permission?

Any help or good read is highly appreciated.