If you have lost your learner's permit, it is illegal for you to drive a vehicle. Failing to replace the permit will prevent you from being able to get your driver's license. You can get a replacement at a local Department of Motor Vehicles (DMV).
Though specific replacement methods vary by state, most require that you apply for one in person at the DMV. If you are under 18, a parent or legal guardian must sign your application form. Some states, such as Maryland, require that a parent or guardian accompany you to the DMV when you apply for a replacement. Proof of identity will be needed to complete the application. Check with the DMV in your state for acceptable forms of identification. In most cases, the replacement will be mailed to your current residence.