"Animated gifs" are a simple form of animation commonly used across the World Wide Web. GIF stands for Graphic Interchange Format. GIF is simply a type of image format that web browsers understand. There are two ways to get animated gifs for your web pages. Find them or make them.
Many of the GIFs from this site come from http://animatedgif.net/ which provides free animated gifs as a sponsored public service to the Web community. There are other GIF animation sites as well. Otherwise, unless the web owner says that gifs on their web pages can be used freely, do not use them unless you have written the web page author and have received permission.
Do you like to read and solve puzzles? If so, learn to use a GIF animation program. This is the much better choice for getting animated gifs, because then you own the animated image. It is also much more fun to make your own then to copy someone else's. Further there is much more personal growth and empowerment from learning to compose your own.
Web sites that teach you how to make GIF animations come and go. Here is one site I found that I liked: http://www.htmlgoodies.com/tutors/animate.html. By searching for "gif animation" tutorial in a web search engine you can find many more such sites.
Learning to animate is learning a powerful way to think. Hopefully you will learn to make them better than the ones that are already on this web site. Also, If you get really good, you can become a teacher, and pass your knowledge on to others!