Pump up the old inner tube and determine the cause of the flat. If there is a hole on the top (the side that faces the tyre) then it could be caused by something poking through the tyre.

If it is a hole on the inside, then check your rim tape. A broken rim tape could cause the spokes to puncture the tube.

If it is on the inside with 2 little holes like a snake-bite, then there is not enough air in the tube and when it compresses and contacts the rims on impact with a curb, it will cause the puncture.

If there is a big tear, then it could be over inflation, causing the tube to dislodge the tyre bead.