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Easier way is to track down the previous owner. A lawyer can make you an affidavit to take to dmv. They have a waiting process you may have to follow.

Hope the car does not have unpaid tickets. The basic process is to have the seller with you, get clearance the vehicle has no tickets then fork over the money and have the tittle transferred. Seller should pay any outstanding tickets / fines before you pay for the vehicle.

I'm with Rey on that one. Before you can register the car on your name all unpaid ticket have to be paid.

Be careful about getting a lawyer if what you want is to track down the owner. 
Sites like ClasificadosPR, Clasificados Online & others usually note the car by the owner the vehicle does not have what they call the "malbete".  That is an indication to the buyer that he/she is liable, "Usually". 
That could mean violation he/she may or may not be aware of violations.  In many cases the new owner might be liable.  In some cases they might even indicate they are selling the vehicle because they are in dire straits which is why the car is being sold. 
If you're looking for the previous owner, I suggest you look up the posting the seller made to be sure you did not accept the terms.  Good Luck.

It's called marbete and it serves as proof that the car has passed a (good for nothing) technical inspection and that the obligatory liability insurance has been paid for a year.
Without marbete you can't take the car on the road - fines for driving a car without a valid marbete are high!

You can easily check if the papers are OK by asking for the license which should be valid (it should be renewed every year and after paying the yearly fee + fines a new license and a new marbete is issued)

Also the official owner is mentioned on the license.

Now, before you give the previous owner a penny, go with them to a colecturia or the DTOP where the car  can officially be transferred in your name. There they check if any unpaid loans with the car as collateral exist and if there are any fines on the car. The seller's ID and your ID (driver's license is best) are checked.
The 'old' owner has to pay fines and if the transfer has gone through you know that the car is officially in your name, you know it's all legal, there are no more fines to pay and you will also receive a title.

Next you can pay the seller and get the car in your possession.

Never ever buy a car and pay the seller without having it transferred in your name!

@Karma7553 Do you at least have the license of the car? Does the car have a valid marbete or sticker on the windshield? You can see the year and month until it's valid.

Without license you have a problem, with the license less of a problem.
Assuming you have a license you can try to contact the person on the license - hopefully it's the guy who sold you the car.
When that's the case tell them you want them to go with you to a colecturia or DTOP office to transfer the title. If he agrees and goes with you he will have to pay any fines and you will get the car in your name.
If there's no valid marbete you will have to get the car inspected and bring the new license that you just obtained. You may have to pay more than one year or marbete fees (around 200 bucks/year for a car).

If you don't have a license or the person on the license is not the guy who sold you the car you need a lawyer. You may end up not owning the car (worst case) or getting the car in your name with help of the lawyer. That procedure involves sending a letter with return receipt to the person on who's name the car is registered and hoping it will come back undeliverable. With that returned letter the lawyer will make an affidavit which you can take to DTOP to get the car in your name. Before they do that you will need  to have the car inspected and then you will have to pay any marbete fees and fines that are on the car.

Good luck!

Hope it is not a stolen car as car would have to go back to victim.
We have several old post telling people to go with seller to transfer and have seller pay any tickets. I guest you did not noticed them.

Me neither

Thankfully after many hours at dtop and the lawyer and piles of papers and stamps .inspection etc. Finally get the car in my name. Wont make that mistake again.

I am glad you got it resolved. Expensive and frustrating experience I beat!