Different manufacturers recommend different break in procedures. For example in what passes for a "manual" that was supplied with my Chinese scooter it recommends the following:

• 0-150km maximum speed 30km/hr
• 151-300km maximum speed 40km/hr
• 301-800km maximum speed 50km/hr
• 801-1500km Maximum speed 60km/hr

Of course the speedometer is calibrated in mph and the odometer reads in miles, so some translation is needed. In round numbers these instructions correspond to

• 0-100 miles max speed 20 mph
• 101-200 miles max speed 25 mph
• 201-500 miles max speed 30 mph
• 501-1000 miles max speed 40 mph

You'd have to be pretty patient to follow that to the letter and really, it's probably not necessary to follow this 100% of the time. You do need to not “top out” your scooter for continuous amount of time, but riding a block or so at top speed once in a while is not going to damage your engine, However riding at top speed for several blocks at a time for extended periods during break in will cause the piston to not “seat” correctly and you will never achieve top performance, and after a couple thousand miles, your compression in the engine will diminish and you will have to replace your engine.

During the break in period try to vary the engine speed as much as possible. It's good to speed up and slow down and not ride at a constant throttle setting for long periods. Also avoid rapid starts and let the engine warm up for about a minute before moving off when you first start the scooter from cold to allow the oil to circulate. This is good advice even after the initial break-in period too.

It's not a good idea to use synthetic oil during the break in period. Good old dino (dinosaur!) oil is what you should use. Synthetic oil may be too slippery and not allow the parts (mainly the piston rings) to "bed in" properly. I'd stick with the manufacturer's recommendation (typically 10-30W) Change your oil when you get it, then every 200 miles until after the break in period of 1000 miles. Then you can switch to a synthetic blend if you want to. Amsoil make a synthetic oil which they claim is specially designed for scooters - see http://www.amsoil.com/storefront/aso.aspx

My break-in technique was to gradually increase speed over the next 200 miles (201-500) and at 500 miles do another oil change. It's cheap insurance. From 500 miles on I've ridden the scooter normally. After break-in the engine oil should be changed at least every 1000 miles as part of normal routine maintenance.

BTW, tires also need a "break-in" period. When new they may have traces of the release compound used during the moulding process on the rubber which can reduce grip. You really need at least 100 miles on a new tire before it achieves maximum grip. Be sure to check tire pressures regularly too, especially over the first few hundred miles, to make sure there are no slow leaks.

Not only the engine and transmission "break-in" over the first few hundred miles. Bolts that have not been properly tightened may work loose. Be sure to go over the engine and frame, checking bolt tightness, fuel and vacuum hose connections and electrical connection blocks after every oil change, this will help keep your bike in great working order.