Choose to travel in the low season to save money on both flights and hotels. Cheap Flights lists the low season as late spring to late fall. Make sure to avoid booking flights during one of the many saints festivals. Prices go up during the festivals even during the low season.
Airlines often offer discounts when you book three or more weeks in advance. You will also get a better seat selection when booking early. Alternately, you can try booking at the last minute through websites such as lastminutetravel.com. Airlines try to sell unsold seats at discount rates though these sites.
The Puerto Rico Channel Online has a flight selection tool that searches 21 airlines for cheap flights to the five airports in Puerto Rico. Make sure to try each of the five Puerto Rico airports, as some may have cheaper flights than others.
Choose to book a round-trip ticket to save money, instead of two one-way tickets. You will have more choice booking a round trip with one of the airlines, like Delta and JetBlue that have daily flights to Puerto Rico.