If a buyer needs to pay in installments. How does this process work for the
seller? Do we get paid at once?
Unless you are financing it (not recommended), you should receive the entire purchase amount before releasing the vehicle. If the buyer is getting a loan, they should give you a certificated check or money order from their bank or credit union.
You are a private seller I gather. You get the check from the bank or credit union where the buyer will make payments. ALWAYS verify funds are available or if the check is good with the bank that issues the check to prevent fraud. It just takes a quick phone call.