Taxing the scooter is easy, just hand you doc's folder to the guy in the tax office payment window and they will tell you the amount. I think you will pay from the begining of the year anyway, for up to 125 it's 36tl for 6 months 72tl for the year, if they will do it now.
The tax periods are January to July and July to January, you only tax for 1 year with the January payment.
I can tax mine online through my bank.