As in any other country, tourists in the Dominican Republic are not legally allowed to work during their stay. If you come into the D.R. with a tourist card and start working without obtaining a work permit or residency, you are violating the law. The fact that many do it doesn't make it legal. Obtaining residency is relatively easy but expensive as Canadian Bob remarked. Renewing your tourist card after its term expires is not a problem: when you go out of the country you will be charged for the extra time.