Can I drive under my foreign license?
If you are legally in the country and have not overstayed your tourist visa (15 days) you will be able to drive under your foreign license.

Can I get my foreign license validated?
The United States Embassy will NOT validate your license. Most European Embassys however, will. If your respective embassy does validate your license, the Department of Motor Vehicles requires the following:

1) A valid license from a foreign country
2) Certification from the foreign country's consular or diplomatic mission in the DR stating that the foreign license is valid
3) Authentication of the certification at the Dominican Ministry of foreign affairs (Sercretaria de estado de Relaciones Exteriores)
4) Passport, valid for at least a year from the time of the application with residency visa or work permit or cedula
5) Payment of fees for medical exam, blood test and license at Banco de Reservas
6) Medical exam and blood test

If my embassy does not validate my license, how can I get a Dominican one?
If your embassy does not validate your license as is with the case with the United States, you will first need a cedula before you can get a license. Assuming you have a cedula, you will have to visit the Department of Motor Vehicles and take a driving test.