If you see a great video showing something you'd love to have in GIF format, here's how to convert it:
[If you need the video (perhaps because you want the audio, too) steps 1-3 would be the way to do it! If you do steps 4-6 to convert to GIF you will no longer have the audio.]
1. Copy the link to the Tweet
2. Go to http://twittervideodownloader.com and paste the link there.
3. Download the video.
4. Go to ezgif.com and upload that video
5. Choose your start and end points. Click to create the GIF.
6. Save your new GIF!!
Here is a video showing the above steps: