Actually, there are 4 providers. Tricom uses CDMA phone, so your Veirzon or Sprint phone would work on tricom after reprogramming. Mind you, Tricom is the 4th player, both in size and influence. The first position, la primicia is being always disputed between Clar and Orange, both GSM networks. They all have roughly the same coverage, though many say Claro has better coverage. I find Orange customer more friendly, and they have cheaper corporate plans. But Claro has better and faster prepaid Blackberry service. They both offer 3G coverage, they both offer prepaid pay-as-you go, fixed prepaid, and postpaid plans. The third company is Viva, formerly Centennial, also a GSM network. No 3G on it. Viva is cheaper on prepaid pay-as-you go, but not that much now as they used to be in the past.
Your best bet is to get a prepaid fixed plan, that way you get very reasonable per-minute rates and after your plan is up you can top up easily. If you bring phone from the USA make sure it is unlocked. An AT&T phone will work on Claro with no problems for 3G (though it will work for GSM calls and EDGE data on all 3 carriers). Most T-Mobile phone (though not all) will work for 3G in Orange (though it will work for GSM calls and EDGE data on all 3 carriers).
You can use any GSM phone on Viva, because it's GSM voice and EDGE data only. No 3G on Viva.
If your phone is CDMA (from Verizon or Sprint in the USA) your only place to activate it will be Tricom. Claro used to have CDMA network as well and they kept activating CDMA phones for some time, but I do not know whether they still activate CDMA phones (they obviously do not sell any now).