Making a GIF usually requires some knowledge of Photoshop or going through the hassle of using some web app that ends up putting an ugly watermark on your GIF.
However a developer has put together an awesome tool that allows you to quickly make a GIF from nearly any YouTube video. The reason I say nearly, is because music videos and other similar copyrighted videos won't work.
The way to do is just to put 'gif' right at the beginning of the URL. Usually a YouTube URL looks like 'youtube.com/watch?v=VpZmIiIXuZ0', you simply put gif at the beginning to get this 'gifyoutube.com/watch?v=VpZmIiIXuZ0'.
You can then choose which part of the video you want to make a GIF of and for how long. It's a neat little tool that makes it much easier to create and share your own GIFs.