If you have just gotten your first scooter, take care. Owning and riding a scooter is completely different from owning a normal automobile.
First, there is the break-in period. On most brand-new scooters, you want to take it easy for the first 300-500 miles. This mean no fast acceleration, and no full throttling. Try to keep your speed under 35 MPH. If you don't do this, you risk damage to the engine.
Always wear a helmet when operating a scooter. This is a no-brainer, or course.
Do a cursory glance of the tires, brakes, and bolts before every ride, as per your scooter manual. This is critical. While a minor malfunction might just mean inconvenience in a regular car, on a scooter, it could mean a serious accident.
We don't want to frighten you. Riding a scooter is extremely fun. Just use some common sense.
Also, you may want to invest in a cover if you don't have a garage to store it in. The elements can do catastrophic damage to a scooter, even if it's just rain. But a good quality cover can prevent 95% of this.