What is the best way to remove enamel paint from kitchen cabinets?

You will find that putting on was a lot easier than taking off. Find citrus based paint stripper wherever you buy paint.

Citristrip a non toxic remover

If the cabinets are real wood and you're not in a hurry, I'd strip off the paint with a citris remover then sand them well. If you desire you could stain them to bring out the beauty of the wood. If not, apply several coats of Kilz2 primer then apply paint. Be sure to number each door and drawer as you remove them. (I number the upper doors on the top hinge side, the lower doors on the bottom hinge side. Drawers are numbered from top to bottom, left to right. - That's just me.) Best of luck.

If you want to repaint them no need to remove the paint.

Make sure they are clean and dry. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint with 120- to 220-grit sandpaper. Use a tack cloth or damp rag to remove dust after sanding. Prime with a stain blocking primer like Zinsser 123, KILZ,or BIN and have it tinted to the color of the top coat. This will prevent dark or stained surfaces from showing through the top coat. Acrylic, or water-base, paints are low-fume and clean up easily with water. Alkyd, or oil-base, paints require good ventilation because the paint contains solvents that can irritate your lungs and make you feel sick. Alkyd options require mineral spirits for cleanup, but they provide a hard, durable paint finish. Whichever you use, buy the best-quality paint you can afford for a lasting kitchen cabinet finish. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.