The way to say 'Please fasten your seatbelt' in Spanish is : 'Por favor, abrochense los cinturones'This is what we usually hear in the airplanes coming from or going to a spanish-speaking destination. The tone is a bit formal.
If you want to tell someone that is coming with you in the car to fasten the seatbelt then it is better to use:
'Por favor abrochate el cinturon'.