This is a chair at a school where I take some classes. Somehow they managed to break it. So this is how I fixed I hope it's helpful if any of your are unfortunate ought to break one.

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Step 1: Materials

drill
1/2 inch paddle bit

1/2 inch dowel wood

glue

painters tape

spring clamps

hobby backsaw

pocket knife

Step 2: Assess the Damage and Glue

Assess the damage and apply wood glue to the broken area, clamp and tape so that it does not move.

Step 3: Drill

Make sure that you have painters tape wrapped all the area that you are
going to drill. If you drill slowly through the painters tape it should keep the wood from chipping out

Step 4: Glue

Whittle down the end of the dowel and apply wood glue. Slide the dowel in to the hole and let it sit and dry. Then take a hobby back saw and carefully cut the excess off.

Step 5: Drill and Glue Again

I decided that this chair needed a little more support then just the first peg that I put in. This time I drilled into another piece of the frame, in the front support of the frame on this chair This piece is covered by upholstery.
I drilled in about three inches through a piece of painters tape. Flip the chair over to get all the saw dust out of the hole, Put glue in the hole and on the peg put the pug in the hole. Wait for the glue to dry and use the hobby back saw to cut off the excess dowel

Step 6: Add More Pegs and Finish

For this specific chair I decided that I needed to put a third peg in. If you want or need to do this just repeat steps 3 and 4.
Remove the painters tape sand it a little bit , put some finish on the pegs so that they blend in, and keep whoeve broke the chair from sitting in it .