In addition to Fair Use, another way to find and use images without asking permission from the owner is to use a Creative Commons search. Images that are ALREADY marked with a Creative Commons license tell you exactly how you can (and can't) use them as well as how you have to cite them.

Search for images without asking permission:

Use Google's Image Search limited to "non-commercial reuse" for the most results! (Go to Tools> Usage Rights)

Use CC Image Search to search and explore images that have already been labeled by license

Creative Commons Licenses and Explanations:

Attribution (by)

You can use the image as long as you give credit to the author

ShareAlike (sa)

You can use the image as long as you share it publicly using the same licenses as the author

NonCommercial (nc)

You can use the image as long as you are not making money from it

NoDerivatives (nd)

You can use the image as long as you do not modify or change it any way

In all, there are 6 different possible licenses. All CC images will feature their license, you just have to copy and paste what it is when you give credit.