Can someone help me figure out how to set Diablo (Classic) to fit my scrren instead of just the upper left corner? I am playing on a desktop and it doesn't fill my screen, I find this rather annoying.

Have you tried with DevilutionX?

My sister had the same issue running the game on her laptop ; updating the graphics drivers fixed it for her.

Try adjusting your monitor to the lowest resolution setting you have prior to launching the game. It was designed to run at 640x480 but 800x600 is as low as my current monitor will go and it looks pretty decent.