Repairing furniture finishes
Point of order, the term enamel is a tricky one. For the purposes of this conversation, lets just say that enamel is the generic name for any paint that has had an additional hardener added to it. Finishes, outside the automotive world, don't really have enamel per say. Not important just clarifying. 

You can go through the process of finding out what your finish is if you want to be thorough (there's any number of resorces on the internet on how to do this) but really when you're refinishing there's only two things to worry about-

A: will the new finish react with the old finish, and

B: will the new finish stick to the old one.

On the first point, its unlikely that you as DIYer (no offense) will have access to anything that will reactivate a descent wood finish, especially a factory finish. That means adhesion is your primary concern. Start with a thorough sanding with 280 to give the existing finish some tooth. If you find any areas where the finish is failing, sand or scrape off the loose bits. Blow off the dust and wipe with a tack cloth or rag dampened with turpentine. Now give it a good coat of a shellac based primer or sanding sealer. Do NOT use paints that have a primer included. They don't cover as well as regular paint, and they definitely don't prime and seal as well as dedicated primers. Plus they aren't shellac based which is what you want because it will stick to almost anything you put it on and will not react with anything you put on top of it. Best of luck!