If you have a gif already you can just upload it. Otherwise you can use software such as photoshop to make a gif out of multiple images. It doesn't really show on the forums here but if you go to a user's profile page, you'll see the image as a gif. For example if you go to my page, you'll see that my avatar is a gif
Basically you have several similar pictures, depending on how smooth you want the animation to be. Then you compile them together under the gif format, which allows all the pictures to exist in the same place and cycle from 0 to the end and return to 0 again. There are online compilers for gif and they're all free. Just google 'gif maker' or something similar to that.
Not sure if you're just restating your question, but I'll answer it again. You just need to upload the image as an animated GIF file, and make sure it's under the 50kb limit. You can make a GIF from scratch using Photoshop or krita (ect.) or you can find one online to use.
A few ways: 1) Get a video and use an online "Video to GIF" converter 2) Get a bunch of pictures and either use a software or online "Image to GIF" to put all the images into a single GIF GIFs are just basically a bunch of images placed into a single file. Think of it as having one of those moving stickman in a book that you see moving when you flip the pages fast enough At 200x200? Nah. Most forums don't even show the full image so I just have mines set at 100x100 which is around the size that most forums use for the user's profile pics