In some states, the license plates stay with the owner. In others, the license plates stay with the car. (Uh, I don't know what kind of "advice" this is, but at least it's an FYI, so know how your state handles this, just so you don't find yourself needing to drive home without plates.)
You probably have from 7 to 30 days to bring the title in and have it transferred. In my state, they fine you $30 (IIRC) extra right at the DVS office (aka DMV) if you're past the deadline, so go in right away.
Make sure there is no lien holder listed on the title, and if there is, that there is a lien release form with the title. (In my state, the lien release form is an official state document with the state seal.)
A written bill of sale (two copies, each signed by both buyer and seller) to accompany the title, helps protect both of you.
On the bill of sale when I sell a car, I usually type out the VIN, year, model, mileage, sale price (and method of payment--cash is safest for the seller), date, my name, the buyer's name and DL number, and "AS IS, NO WARRANTY," and then we both sign and date both copies. It's a simple step and as a seller, it protects me if the buyer doesn't transfer the title and starts getting parking tickets or committing crimes in my old car. As a buyer, it serves as a verification the DVS/DMV of the sale price in case it's unusually low and they think you're trying to evade sales tax. (Eg: I bought a 9 year old car for $200, but I didn't have a bill of sale, and when I went to transfer the title, the lady said "sorry, I've got to look this one up." I ended up paying $70 sales tax because the $200 POS "booked" for $1100.)