Take off the back of your chair from the rear portion of your chair's seat. To do this, put glue solvent around the lower part of your slats to cause the glue that each hole contains to become less secure. Then, remove the slats one by one.
Place your chair in an upside down position. Put additional glue solvent along the upper parts of the legs of your chair, so you can remove them easily.
Trace the shape of your chair's seat so that you know how much material you have to use to insert a new seat.
Slice off a piece of wood in the shape you require to put a new seat in the position of your old one. You can use a jigsaw to complete this part of the process. Smooth the surface with sand paper and utilize your paper of the tracing variety to designate where each slat needs to go.
Use your drill to place openings in the places you just marked and add a good portion of wood glue in every opening. This enables you to connect the legs and back of your chair once again.