NOT REALLY A BOX; JUST TIDBITS OF INFO

THE FINISH TEST
Before slathering anything all over a piece of furniture, determine what finish needs to be removed and then buy the solvent that will do the job. Try this test on a small area (that won't be seen later) to determine what type of finish was used.
First, wipe a small drop of rubbing alcohol on the finish with a cotton ball or a clean rag. If it's shellac, the spot will soften and get sticky.
If nothing happens, next try a spot of nail polish remover or anything else with acetone in it. If the finish gets soft, it is lacquer.
If nothing happens with rubbing alcohol or acetone, it's safe to say the finish is varnish, but varnish is rare.
COMMON MISTAKES
Refinishing a piece of wood furniture is a two-part procedure. The first involves stripping the old finish, and the second involves applying the new one. In theory, there is little room for error in either. But that's in theory.
One of the most common errors people make when refinishing their own furniture is to not clean off all the stripper. Strippers contain wax. Wiping on a coat of alcohol will help get rid of the wax, but it is important to get as much of the residue off as possible. Slow down and clean the surface thoroughly. Otherwise, the wax residue will affect the application of the new finish.
Another common error is to put on too thick a coat of finish at once. You may be guilty of doing this in the interest of trying to get the job done quickly. A thick layer can cause the finish to dry, crack, peel, flake, or run in thick, wormy waves, creating more mess to remove.
Chemical combinations in commercial strippers and finishes vary, so whether you are stripping old finish or applying new finish, it is very important to follow the directions on the can.
Note that refinishing a piece of furniture won't make woobly legs sounder. Reglue loose points before you strip, not after. Yellow carpenter's glue works well for all joints because it is strong and slow to dry (approximately 24 hours), giving you plenty of time to adjust the piece and clamp it with a C-clamp. (Epoxy works for very small repairs that you can hold in place, but remember that the five-minute kind sets up very quickly, so you may want to use the longer-setting epoxy.)
WHAT ABOUT KITS?
Entire industries have been built on the theory that not everyone who needs to do something has the time or inclination to research the basics and assemble what's needed. Enter furniture stripping kits, which are sold at hardware or paint stores for about $20 and claim to have everything. They may even lure you with a color photograph of a loving couple admiring their beautiful, gleaming, refinished piece - after all the messy work is done.
Typically, a kit contains a chemical stripper in pint-or quart size bottles, steel wool or abrasive pads, and instructions. Some kits also include a plastic tray for mixing, rubber gloves, a can of stain or wool filler, and a mixing stick - convenient, perhaps, but none of these extras are what you'd call industrial grade. (In fact, the mixing stick is usually Popsicle grade.)
The chemicals in any refinishing kit will most likely contain the three main stripping chemicals; the stripping properties of each chemical are not changed by the presence of the other two.
Even though you may be buying more chemical power than your finish needs, most kits work well enough for a small piece. But if you are going to refinish something large, like a dining room table, you will be running back to the hardware store four or five times for additional kits before you are finished.
A much easier and more cost-efficient method is to determine what the finish is and buy only the solvent you need.
BEWARE OF DIPPING
Another method of having a finish removed is to send it out to a place to be dipped. The furniture is immersed in a vat of harsh chemicals, and then the finish is sprayed off with a blast of water or another solvent. While some intricate or very heavy finishes may benefit from dipping, it is generally not a good thing to do a piece as a whole.
A dipped piece often comes out of the vat with its joints loosened and its surface very rough. It will need a lot of sanding to make it smooth and ready for a new finish. (Dipping is frequently resorted to by old-house restorers wishing to save heavily painted doors or windows.) The quality provided by dippers varies. Antiques dealers usually have the inside scoop on who does a good job.
MAYBE IT'S JUST DIRTY
A piece that you think needs refinishing may be better served by just a good cleaning. Use paste wax, applied with a soft nylon scrub pad or a coarse rag. (The wood shines with a rich, mellow patina afterward.) Try this before deciding to take on a more involved project.