The trigger ring simply snaps onto the crankshaft. Just align the tab on the trigger ring with the recess in the base of the crank.
Insert the key into the slot of the crank, and carefully place the flywheel back on, aligning the slot in the flywheel with the key.
The key is what sets the timing.
Is it actually backfiring (through the carb), or after firing (out the exhaust)?
When was the last time you installed new spark plugs and adjusted the valves?
It is a long shot, but if it backfired that hard, it is possible that it spun the gear on either the crankshaft or camshaft.
The engine would need to be disassembled to verify this.
If you want to dig that deep, I can upload a manual for you.
Click here to download.