The fix begins by forcing wood glue into the crack and clamping the seat back together.
Repair split wooden chair seat.
How to repair cracks in a chair seat.
While this will put the chair back together it may happen again.
Step 3 joining the split.
If you split the rear legs or your seat is shield shaped try using a band clamp around the seat to close the split.
The seat must be completely removed for doweling.
With the seat clamped up reassemble the chair.
Instead they glue planks together edge to edge to form a single plank wide enough.
Split chair seats can be repaired with a series of 1 8 inch dowels wooden pegs along the break and reinforced with metal mending plates.
Then add some pressure across the grain anywhere you can get a clamp to hold.
Drill holes for the dowels in each side of the broken seat about 1 inch deep or as deep as possible and spaced about 4 to 6 inches apart.
Use a wood stir stick to have more leverage and to protect the finish of the wood from scratches and dents.
A split seat on a wooden chair often sends it to the junk heap but this solution may save one at your house.