Oh boy I love me a scooter issue!
If it's a flooded engine, sometimes letting it sit for a day or two will be enough to get it running. If not, here's some basic troubleshooting I do:
-- Shoot some carb cleaner into the carburetor. One end of the carb goes into the engine, the other end goes into the air box. I'll usually disconnect the air box end then shoot it in. If the engine fires but does not run, it's a fuel issue. Most likely a clogged carb, bad fuel, or bad fuel filter.
-- If the scooter did not fire with carb cleaner, I'd step up to a quick shot of starting fluid (careful, this stuff can get fiery fast). If neither netted any firing of the engine, your issue is spark. Since you have no battery, that's going to be your magneto, spark plug, and coil.
-- If none of the above works, check compression. No compression, no start.