What kind of chairs are you working on? I'm going to assume they are late 19th century or early 20th century factory made chairs. If so, the parts of the seat will be held together by dowels, two per joint, probably 3/8" or 7/16".
The first issue is to decide which joints need to be disassembled. For me, it's any joint that you can move the joined pieces relative to each other. Almost always, the back chair joint is loose, meaning that if you grab the back of the chair and push and pull it, the back moves relative to the seat (meaning that back joint is loose). Any joint that doesn't move should be left alone.
The next problem is to get the joint apart. Before you take the joints apart, TAKE PICTURES. You'll be amazed that you can forget how the chair goes together. Also mark the pieces - left, right, front, left leg, right leg. Left and right is as you are sitting in the chair. It also helps on the side rails to mark them "front joint" and "back joint" so you don't try to put them together backwards - don't ask why I recommend that.
You can pound on the pieces or use a clamp in reverse to push them apart, but doing so risks breaking the wood. If the joint is loose, I use a flush cut saw and cut the dowels always being careful not to cut the wood along the visible seam. If you're going to mark the wood with the saw, do it on the inside of the seat where it won't be seen when re-glued.
Use a drill one size smaller than the dowel and drill out the dowels. So if you have a 7/16" dowel, use a 3/8" drill. Use a small (1/8") chisel and remove the rest of the dowel along the side of the mortise. If you're careful, you can re-assemble with the same size dowel.
If you want to do a trial fitting, cut yourself some short dowels - maybe an inch - and do the trial fitting. You don't want to use full length dowels because they're hard to get out and you haven't put any glue on them yet.
For your real glue up, measure the holes carefully and cut your dowels a bit shorter. Remember that on the front legs, one dowel will likely interfer with the dowel from the other joint so allow for that space.
To glue up, use slow epoxy - not fast for a bunch of reasons - you want to have plenty of time to do everything and slow epoxy is stronger.
That's about it.
Mike