How can I upload a video which shows working of my design instead of just a fixed image.

If you search GIF in the tutorials here at GrabCAD there are many good tutorials on how to convert video to GIF using various software or online converters.

Record the video, using any good screen recorder edit and then simply upload....

Yup,
I agree with Mark and trinity.
You just have to decide how you want to upload your "video".
Do you want an animated gif which shows motion and auto loads, or do you want a link to Youtube page?

See just about any of Trinity's projects for a great example of the animated gifs: https://grabcad.com/library/laser-cut-windmill-wooden-toy-1

If you upload 10 projects, and use the URL link option for a video, you can get yourself a shiny badge for your profile.

Hi there, I think you could use a screen recorder to capture your videos first, and then upload them to the platform you want. As for screen recorder, if you only need to record screen for once and have no need for further editings, you can press Win+G to open Windows 10's built-in Xbox DVR (if you are running Windows 10). My friends told me that PowerPoint can be used to record video as well, but I never really try. You could check it if you need. If you would like to have more professional recording functions, I'd recommend Joyoshare Screen Recorder to you. I'm a big fan of it. It can help you record in 1080P in no lag, so that you don't have to worry that your recorded videos would be too annoying to watch. I've used it for a long time but haven't found any defect yet. Share it here in hope that it could be useful to you. Just to add, you could adjust output format of you recordings so that they could compatible with any platform you like.