Put scooter in a warm, dry area if possible. In the sunshine, a heated garage etc give the scooter as long as you can to dry out, a couple days if possible.
Remove carb and drain of gas and water
Get some gas treatment for the tank, STP and Gum Out make this. This should remove any water in the tank if the tank was not fully submerged. If the tank was fully submerged you will need to remove it from the scooter, drain it and dispose of the gas/water mixture correctly. Allow to dry before putting in fresh gas, and use some Gas Treatment anyway for excess water in the fuel line.
Drain the gearbox oil of oil/water. Allow to dry before putting more oil in. Once the scooter is dry and running you might need to fill and drain the gearbox several times to get any water residue out. If your oil turns milky or frothy after running you still have water in transmission somewhere.
Remove spark plug and exhaust if possible. Kick scooter over to push water out of top end, drain exhaust if you can, if you can’t remove it, kicking the scooter over should push enough through so that the scooter can start, which will force the rest of the water out. Put some 2 stroke (a small amount) into the top end and kick over again to protect the bearings and crank and piston while the scooter sits for a couple days drying out.
Remove the flywheel and use a hair dryer on low setting to dry the stator out. If you can’t do that, removing the flywheel at least with the engine in a warm place will help dry the stator out.
You can check for a spark before trying to get the engine started – put the spark plug into its cap, and, holding the plastic lead or cap, rest the end of the spark plug against a piece of metal and kick the scooter over – if all is good you should see a spark on the plug.
Reassemble everything. Put in some new transmission oil and gas and see if the engine will fire up!
Letting the scooter idle for awhile will bring it up in temperature and will help to dry out other parts of the engine