Screencasting with Animated Gifs in mind must be kept short - 20 seconds or less. This can be a struggle but forces one to target the video to specific actions.
More often than not you will be sharing the Gifs on Google+ but sharing a link does not do the Gif justice. After you contruct the Gif it is automatically saved to your Google Drive. I would not select download or link to share on Google+.
If you have not shared the Gif previously, share it by Share Google Photos - Google Drive and search for .gif.
If, on the other hand, you have previously shared it in a post, simply Share Google Photos - Photos and select your Gif.