I basically do not prepare for it. Either I know the answer or I do not. The vast majority of problems I face are of unknown scope at first and I have to acquire knowledge before tackling them. If I don't know the answer I try to present my thought processes and how I think about it and possible problems.

I read up the company and their technology to maybe get an idea about the problems they need to solve.

don't prepare. If you go unprepared, and freak out of get backed into a corner, expect the job to be that way.