Corey, if you use the search function on this site, you will find all the information you need.
Basically, the pets need health certificates obtained from your veterinarian. All their shots must be up to date and prior to 30 days before traveling. Secondly, you need to speak with your airline. There is a limit to how many pets may fly on a plane at a time, either in cargo or in the cabin. If you will fly your animals in the cabin, they must ride under the seat in an airline approved container. You must have a "reservation" for them and pay for them to ride The cost is different for each airline. If the pets will travel in cargo, you must adhere to the embargo dates. Check with the airline, and follow their regulations for approved containers for embargo. Once in the DR, you must take your pets to the inspector at customs for agriculture. He will inspect your paperwork and provide you with a form to show your pets are permitted to enter the country. The cost for this for my small dog was 300 pesos. If you return to the States with the animals, the process is somewhat similar, but in reverse.
Good luck.
Lindsey