how do you get those ksp challenge completing pics?

[KSP Bro AE]

I have no idea how it is done. I see basically everyone hase them, but how does it work?

[Cairol]

I guess after you proved your successful completion in the respective challenge thread, the author of the challenge acknowledges that.
And then you are allowed to copy the badge from the challenge thread. It's usually provided in the first post if there is a badge.
So you can insert it in your signature if you want.