same as when I bought my last used car from a private party. We went to a branch of the sellers bank. I wrote her a check, teller then verified funds and transferred the amount from my banks bank account to her bank account. Took all of a few minutes.
Now be aware that a transaction of the amount the OP is talking about is not usually an "instant" transfer. Banks are allowed several days for amounts this large. so if you just verify the check, then go to deposit it in your bank, there is time for the other party to try to stop payment. If both of you have the same bank, it's easy peasy for the bank to do the transfer as you wait. Otherwise go to your bank and have them do the transfer BEFORE you sign the title.