Here are the steps that I followed:
1. Download video from Youtube using Chrome's Youtube plugin. It will get downloaded in MP4 format.
2. Convert from MP4 format to MOV using the command (in a Linux/Mac terminal):
ffmpeg -i input.mp4 -f mov -vcodec copy -acodec copy output.mov
3. Import the MOV file in Adobe Photoshop using the "File -> Import -> Video Frames to Layers" option and select the section of the video that you want to convert to GIF.
4. Resize to desired size using "Image -> Image Size" option
5. Export as GIF using "File -> Save for Web and Devices" option. Select the required GIF settings and click "Save"
6. If you want to upload to the web: My favorite image sharing website www.imgur.com has 2 MB limit on GIF upload size. For GIFs greater than 2 MB, you can use www.min.us.