Complete the application required by your state for a copy of your car title. The information varies slightly from one state to another, but the forms in Texas (VTR-34) and California (Reg 227) as of 2015 ask for the car's VIN and the applicant's driver's license number.
Make the application in person or through the mail. The fees are generally nominal, as in Texas the cost is $2 through the mail or $5.45 in person. In some states, you may have to submit a photocopy of your driver's license with your application.
Most often, people need a copy of their title because they have lost the original, or it has been stolen or damaged. In California, the application includes an explanation for the reason for the request -- an explanation of what happened to the original title to the car.
If you still have an outstanding loan on the car, the request for a copy of the title must go through the lienholder. If you have paid off the loan, the lender should send you the original title, so you don't need to request it from the state. If you have not received your title from the lender within 30 days, contact them before applying for a new copy.