Is it for when you will register a vehicle in New York at a DMV office?
No.
What do I need to do when I've bought my car from some guy online?
In this situation, both you the buyer and the seller must complete the Statement of Transaction {Sales Tax Form} at NY State Department of Tax and Finance DTF-802. Then you will bring the form to a DMV office where they will calculate and collect the sales tax, and also issue a sales tax receipt.
What other documents do I need to bring if I bought a car from a NY car dealer?
In that case bring the dealer 's bill of sale that shows that you paid NY State sales tax.
Are there any other tax payments involved when I register this car?
Yes, you probably also will need to pay county use tax when you register your vehicle.
I've heard about exemptions or deferrals of sales tax, who's eligible for that?