The go to the office of the Electoral junta where they were born, with proof of birth and get it on the spot. At age 18. If they don't have one they cannot vote and in some places the cops are pretty insistent they have their cedula with them if asked.
I am surprised the Dominican you are asking about does not know where in the home town the cedula office is unless they don't have one as they are merely saying they are 18 and they are really younger. Watch for that.
It has to be easy and relatively simple paperwork as some of the most clueless girls I have met obtained them in a one visit exercise and if it were complicated as say showing up on time (within 3 hours), telling the truth, or wearing proper clothes they'd be unable to do it.