Getting in and out of the airport is pretty easy.   Everyone (except Dominican Born and Legal Residents) must have the tourist card $10 per person, even for babies.  You can buy this as you enter the customs hall or the Tourist Card can also be purchased in advance on line for $10 USD or 10 BPS, https://www.dgii.gov.do/Tturistaweb/  Just print it out and you are ready to go, no names of signatures needed.Then you turn it in at passport control. Fill out the forms given to you on the airplane and give them to the immigration officials. Then collect your baggage and  go thru customs and on to the exit. There are many porters who want to help with your luggage, if you don't need help just say, "no, gracias".  Some may ignore your request just smile and keep walking.  Leaving Customs walk to the waiting area where you will find the travel agency reps for groups and Taxis if you need one. It’s not a far walk. 

When it comes time to leave you will need to go to the ticket counters. They will give you your exit forms to fill out and will check your bags. Your hand held bags may be checked by the Agriculture control and/or extra security screening. Then your tickets and passports will be screened as you enter security and the departure area of customs.  Be advised that most liquids and extra batteries should be in your checked bags as they may be confiscated at security. The rules are a little different here than at home.

Many of the tour operators include the arrival tax or departure tax in your package. Have $10 available at arrival and $20 available at departure, per person if this applies to you. At this writing, most Canadian packages (except Sunwing/Signature) include both fees. Also, all U.S Airlines tickets include the $20 departure tax. Be well informed about what your package includes and only pay the money if asked. Don't just hand it over! Feel free to use the luggage handlers if you feel you need them. They are not ALL land sharks out to get you. When you need a helping hand, they're there. If you don't need them, keep going and say a confident  "no, gracias!" Once you go throught the Customs area you will find the duty free shops and a few eateries a bar and the departure gates.