... on Bad Penny. Or at least performed by me, I should say. It likely had two before I got it.
Here's what you need to do an oil change on a scooter (any 4-stroke scooter, pretty much); clockwise from upper right:
c.) Socket wrench w/17mm socket;
d.) Nasty-ass t-shirt, or similar not-completely-disgustingly-oily rag;
Look underneath your scooter. If you don't see this 17mm bolt with a huge flange on it, you may have a 2-stroke. Otherwise, this be your oil drain plug. It's typically found at the lowest level of the crankcase. Unscrew and remove the oil dipstick from the bike, setting it on the nasty-ass t-shirt for now. Making sure your socket wrench is set to apply force in a counter-clockwise manner, affix said wrench (with 17mm socket applied) to the drain plug, and grunt a little. Break it loose, and make sure you have your catch basin strategically placed in a position where gravity +/- wind will carry the stream of old oil into it. Once that is done, remove the drain plug, completely.
Check the level with the dipstick. If anything, you want there to be only as much or slightly less oil in the crankcase than specified in your owner's manual at this point. If that is the case, replace the dipstick and tighten, wipe your oily hands on the nasty-ass t-shirt (you don't want oil on your throttle handle, keys, etc.... trust me), and start the engine.
Let the engine run for 2-4 minutes, checking for drips or leaks. Don't be fooled -- on some bikes, the centerstand is directly in the path of the old oil that you just drained, and if you didn't observe this and wipe everything down with the nasty-ass t-shirt, you might see a little dripping. Always make sure you identify the source of any drips, though... you do not want any oil coming from the area where the drain plug meets up with the crankcase. If that is the case, refer to the owner's manual, and apply appropriate torque to the drain plug using a torque wrench. If the dripping continues from this area after that, do not run the engine until a mechanic has checked it out. Running out of oil is VERY bad mojo.
After the engine has run a few minutes, shut it off, and again, check the oil level. Add oil if needed, carefully re-checking as you add. Do not overfill the crankcase! If you do, you'll need to drain that costly new oil out, and start over.