Yes Podster, My chairs are just like these only mine are a darker brown. I did have 6 chairs, but my DH broke one, so now I have 5. My table is not like the one in the picture.
I saw my complete set which is in white, (love to have that)
They are very pretty. Do you have your fabric already?
That is called a french back or a cameo back on that type of chair. It is removed from the front and the back is either attached to the frame first from the front. Or the back, padding and front are assembled together and installed from the front.
I wasn't able to see the trim around the front of that chair back well but it will probably have a gimp trim, a matching fabric welting or piping or a wood trim that will need to be removed first.
First, look around and find someone that does upholstery. Find out how much they would charge.
Then, tackle it yourself. If you aren't successful with the first one, you can always fall back on the upholsterer.
It is not a great mystery and if you sew you will grasp the concept of upholstery. The first chair I did was a vintage overstuffed rocking chair that I bought for $20. The 2nd hand store had a pair of them but DH said no ~ just try one first. He was so impressed that I managed to do it that he went back to buy the second one but it was gone.
When you disassemble it, save all the pieces and take notes and number the pieces if you feel you need to in order to help you remember the steps. Do not tear up the fabric but use it for a pattern to cut the new fabric. If you need new supplies like tacks or gimp you may have to order it but that is not a problem.
Is the fabric on the chairs in bad shape? How badly is the broken chair? Can it be repaired? I hope you still have it, you might experiment with that chair first.
No, I threw away the chair years ago when my DH broke it, We don't have much storage around here, but that would have been a good idea. I use to do some sewing and some craft projects, but never took furniture apart except the bottom part of a chair, that was easy. By the way, they just used regular trim,that you buy at the fabric store. no problem replacing that.
Start by carefully peeling that trim back and you will see how the front piece of fabric is attached.
It is probably tacked or stapled to the wooden frame. There is a tool that easily pulls staples or tacks.
I just realized I have a chair that has an egg shape back on it. I'll have to check it tomorrow, because I'm getting to tired to do anything else tonight. I'm going to lay down now and watch the Titantic until I fall asleep. Thanks and goodnight.