Here's what you will need:
- A cheap metal compact mirror (see below)
- Cheap white nail polish
- An image of whatever you want on your compact
- Good quality top coat (something like Seche Vite)
- (Optional) Mod Podge Dimensional Magic
- You might also need box cutter and/or acetone
If you are patient you can put some acetone in a shallow dish, open the compact and let the acrylic top soak in acetone for 10 minutes or so (make sure the seam is submerged, but try to avoid letting acetone getting into the mirror side). It should come off easily.
There is a white sticker between the acrylic (it's actually clear) and the metal. Peel it off and keep the acrylic as a template.
Prepare the image you want to use on the compact. It can be a photo, magazine cut out, collage, even fabric. Some hardware stores or home decorating stores give out free wallpaper or upholstery fabric samples, you can use those too. Use the acrylic top or the sticker as a template to cut out a circle.
Next paint the entire surface inside the frame with white nail polish. It doesn't have to be perfect.
If you want a smooth acrylic "dome" top, you can use either Mod Podge Dimensional Magic or jewelry resin (both available at craft stores) on top of the clear top coat (using it directly on top of the paper might lift some of the ink off).