The primary requirement for furniture work is patience. Nowhere is this characteristic needed more than in stripping furniture. Let's see if we can make this messy task any easier.
First, what do you need? Specific items will vary from piece to piece, but the following list should get you through most jobs. You'll need stripper, of course. What kind? You basically have two options, and then two choices within each option. Here are the options. If you're really keen on the environment, you'll want a water-base stripper. They work fine, and as the label suggests, you can wash the residue off with water. The downside is that using a water based stripper means you must sand the piece completely before you do anything else. A solvent based stripper doesn't raise the grain of the wood, but you have to be more careful with it. Sanding is kept to a minimum. Whether you choose water or solvent base, your next choice is going to be liquid or semi-paste. Liquid usually strips faster, but the semi-paste is excellent for adhering to vertical surfaces and carved material to remove the old finish from all the cracks and crevices.
Other items you'll need include a flexible blade drywall knife, 3", with a dull edge and slightly rounded corners. No, you can't buy it that way, except for the 3" and flexible part. Dull the edge and round the corners slightly with a file. This will help prevent gouging the wood when you scrape off the old finish. Steel wool, both XX and 00 grades, to help remove what the putty knife doesn't get, as well as to work on carvings and legs. Industrial grade rubber gloves. The kind sold for washing dishes won't last - don't bother. When I worked where cotton rags were plentiful and cheap, that's what I used. Now I use paper towels, and buy them in the 12 pack when they're on special. If you're using a solvent base stripper, you'll also need some lacquer thinner - a quart will be plenty for the average piece. Get a natural bristle brush, not synthetic, preferably the cheapest one you can find, 2" wide, for applying the stripper. Lots of old newspapers to cover the floor under and around the area you're working in and a quart of paint thinner. If you buy a length of 3/8" or 5/16" dowel rod and cut it into 5-6" lengths and then run both ends through a pencil sharpener, you'll have some great tools for digging in cracks and crevices that won't chew up the wood. Some disposable foil pans for pouring the stripper into and catching the mess as it comes off will also be handy.
Now what? A well lit and well ventilated area to work in; old clothes that you can afford to throw away if necessary; and patience. Every stripper I've seen says put it on (in such-and-such manner) and let it stand for at least 15 minutes...and nobody does. Read the directions and follow them. The people that made the stuff know more about it than you do. They put directions on the can so you'll get good results and use their product again, instead of something else. If you don't have a watch, borrow one. Time yourself when applying stripper. It will save you a lot of work and frustration in the future.
By the way, the paint thinner is used to clean the piece before you do anything else. Stripper won't cut through grease, oil, or wax. Paint thinner will remove them all. The lacquer thinner is used as a final wash (with solvent strippers) after you've finished stripping. It will remove the last traces of stripper (so it won't attack the new finish) and will neutralize any left in the cracks and crevices.