Stripping and refinishing is not too hard, but it's tough to explain in a short post.

Strpping
Best to use a chemical stripper containing methylene chloride, the most effective stripper. Almost all strippers contain this except the "green" ones like Citristrip. Nothing wrong with the NMP strippers except they are much slower acting and might need multiple applications. Apply in a well ventilated area like an open garage or carport if you have one. Apply, LET IT HAVE TIME TO WORK (don't believe the instructions if they say fast acting). If needed, you can apply some sheet plastic over the top to keep the stripper from evaporating away. I'd allow at least an hour. Scrape off the stripper with a plastic putty knife, wipe with rags, and I usually rinse with acetone (again, in a well-ventilated area). Allow to dry overnight.

Sanding
Do a LIGHT sanding, particularly if veneered, which it probably is. On solid wood edging, apron and legs, you can get a little more aggressive, if needed, to get rid of splintering and scrapes.

Stain
Stain is optional, depending upon base woods. If it's mahogany or cherry, it will look like mahogany or cherry, so there's not need to apply a mahogany or cherry stain :-)

Finish:
This is really up to you. Probably the most foolproof for a novice is a wipe-on varnish. General Finishes' Arm-R-Seal is a decent one.

If you have decent library nearby, look for "Understanding Wood FInising" by Bob Flexner, author of the book below.

Here is a link that might be useful: http://www.popularwoodworking.com/techniques/finishing/finishing-for-first-timers

Thanks for the detailed response!

I've been afraid to somehow 'ruin' my table, with a stripper though I know it's not a super valuable antique.

I've done a lot of sanding and refininshing painted surfaces, and I've done floor sanding and refinishing with polyurethane, but never 'nice' furniture and never with a stripper.

I do have a carport, and with PA's high humidity I don't think the stripper evaporating away will be a problem.

It seems silly to strip it uness I'm ready to refinish so that I don't have the same problem. Thanks for the link.