Example:
Image source: Corgi Puppies 18, by Flickr user Daniel Stockman. Used with permission under a CC BY-SA 2.0 license.
Most images (and text too!) are copyrighted, even if you don't see the © symbol on it. Something in a tangible format is copyrighted by default. This means you need permission to use them.
Because getting permission can be time-consuming, I recommend you use Creative Commons images instead. They're free, and permission to use them is built-in.
The Creative Commons came about as an alternative to traditional copyright. They developed several legal licenses (below). While each license has its own set of rules, they also give a lot more freedom than traditional copyright, and they're written in plain language, so they're easier to understand.
This license lets others distribute, remix, tweak, and build upon your work, even commercially, as long as they credit you for the original creation. This is the most accommodating of licenses offered. Recommended for maximum dissemination and use of licensed materials.
This license lets others remix, tweak, and build upon your work even for commercial purposes, as long as they credit you and license their new creations under the identical terms. This license is often compared to “copyleft” free and open source software licenses. All new works based on yours will carry the same license, so any derivatives will also allow commercial use. This is the license used by Wikipedia, and is recommended for materials that would benefit from incorporating content from Wikipedia and similarly licensed projects.
This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to you.
This license lets others remix, tweak, and build upon your work non-commercially, and although their new works must also acknowledge you and be non-commercial, they don’t have to license their derivative works on the same terms.
This license lets others remix, tweak, and build upon your work non-commercially, as long as they credit you and license their new creations under the identical terms.
This license is the most restrictive of our six main licenses, only allowing others to download your works and share them with others as long as they credit you, but they can’t change them in any way or use them commercially.
Items come into the public domain in a variety of ways. One option is for creators to "dedicate" their items to the public domain. This simply means they choose to waive their copyrights. The CC0 license refers to items that have been "dedicated" to the public domain.
Google Images is probably the easiest place to start.
First, search for your topic. Then, click Tools at the top of your results. Use the Usage Rights drop-down menu, and select Creative Commons licenses.
Here are a few specific sites you may want to explore as well:
Attribution (CC BY) 
Attribution-ShareAlike (CC BY-SA) 
Attribution-NoDerivs (CC BY-ND) 
Attribution-NonCommercial (CC BY-NC) 
Attribution-NonCommercial-ShareAlike (CC BY-NC-SA) 
Attribution-NonCommercial-NonDerivs (CC BY-NC-ND)
Public Domain (CC0)