You can visit the New York State Department of Taxation and Finance website.
Will that site give me more information than I can get by conversing with you like this?
You can go to that website for more information, yes.
Are there sales taxes both on vehicle purchase and on vehicle registration with the DMV?
The DMV does not collect sales tax when you apply for a vehicle registration if NY State sales tax was paid to a NY State dealer and will, for that reason, not issue a sales tax receipt.
What will I need to do when I register my vehicle in New York at a DMV office as far as sales taxes?
When you register your vehicle you must either pay the sales tax, prove that the sales tax was paid, or prove that your vehicle registration is exempt from sales tax.
What is the procedure if I was not a resident of New York when I bought my car?
You will use the Sales Tax Ememption form at NY State Department of Tax and Finance DTF-803 to receive a non-resident exemption from NY State sales tax.
What proofs will I need to transfer my title to a NY State title?
If the name on your title will not change, then sales tax forms and proofs are not required.
Does it matter if my car was a gift to me?