How do I paint a mirror to look professional?

I have mirrored closet doors that cover a whole wall. I don't want my "den" to look like a bedroom.

Why don't you use etching cream to change their look? You can do it temporarily with frosted contact paper or get the etching cream at the craft store. You could make horizontal lines across it or use a large stencil for an image like a fleur de lis, Japanese or chinese symbol, say like the one for success. If you use the contact paper you simply cut the shape out, remove the backing, stick it to the glass, smooth with a credit card. If you use the etching cream you will either have to tape off your design or use a stencil that is well adhered to the glass. Fill the image in, leave it for the time indicated and wipe it off. Viola, a professional look!

I had the same set up in a place I rented. The mirrors bothered my wife - I won't go into why that was. I took them down and put them in storage and just hung multiple drapery panels.

Covering the mirrors with paint won't work on its own. You would have to use a chemical etcher first to make a surface that can be painted. Even then, it won't look that great...it'll look like mirrors covered with paint.

You might want to try decorative film on the mirrors... make it look like a cloth texture or stained glass, this would be cheaper than replacing the doors, and it can be removed in the future if you want to change back to the mirrored look.