1989 Toyota Corolla Window repairs

You would need to pull the inside door panel, which for this year Toyota is not too hard.
The windows are bolted in. You would be better off finding used windows at a junk yard (like U Pull It).

You would also need to inspect the regulator to make sure it is not broken.

I would not use plexiglass or a plastic material, since it would be a permanent install (you could not roll down the window, which would be a saftey hazard and probably illegal.