For chairs like this I would recommend dip-stripping. Test all the joints first if solid you should be ok. After you have your chairs back from the stripper, go over with a course steel wool and ending up with a 00 or 000 steel wool for the final sanding. Before staining I would recommend minwax sand and sealer as your first coat.
Also better to try your stain first on the underside of the seat. After stripping and sanding the stain will soak in and if you dont like the color , you can adjust it in this area first.

Thank you!!

Unless you remove every bit of the old finish, the new stain won't penetrate the wood and either will look uneven or the finish won't do what you want. Your choice is either have them dipped or do the painstaking job your self.....which is really a lot of work....trust me after one chair you will wonder why you started....all those spindles? Oy!

But why are you refinishing them? They look in great shape to me.
If you simply want a different tone to them....you would be better served to put a colored finish over the existing finish....roughing a bit with sand paper so it sticks.