Verizon has service in Puerto Rico, although they do not have stores in Puerto Rico. Verizon calls, text, and data fall under their Nationwide and More Everything calling plans, so you should not be charged extra for roaming while in PR. Verizon Wireless stores and towers are not in Puerto Rico, after having sold their towers to Claro in 2007. However, Puerto Rico does have stores for the US based majors like AT&T, Sprint, T-Mobile, as well Latin American providers such as Claro, Open Mobile.
Making and receiving phone calls, text are considered domestic and are covered under your calling plan. If you do not have a text messaging plan you are then billed $.20 cents to send and $.20 cents to receive. Please keep in mind, sending and receiving picture or video messages are not covered while in Puerto Rico and the charge is $.50 cents to send and $.25 cents to receive.
Data usage in Puerto Rico is considered domestic and will deduct from your current data plan. Also, please keep in mind that Puerto Rico is part of the Extended Network, which means Verizon has agreements with other cell carriers in the area to allow Verizon customers to use for service.