Old San Juan is walking territory. The historic core is small enough that you cover it on foot, with the city's free trolley filling in when your legs give out — look for "Parada" stops on every other corner.
Beyond the old city, ride-share is the default. Uber works well everywhere in metro San Juan and is the easiest way to move between Old San Juan, Condado, Ocean Park, Isla Verde, and Santurce. Set a budget of 15–25 dollars for most cross-city rides. Tourist taxis (white, with a sentry-box logo) charge fixed rates between the airport, Old San Juan, and the resort strip — they are convenient but more expensive than Uber.
Public buses (AMA) are cheap (a few dollars) and run on most major routes but are unreliable and slow. Skip them unless you have time to spare. The Tren Urbano elevated metro is useful for trips to Hato Rey (Plaza Las Américas) and Bayamón, but does not reach Old San Juan or the beaches.
The Luis Muñoz Marín International Airport (SJU) is 15 minutes by taxi or Uber from Old San Juan, about 10 from Isla Verde. Driving is fine for excursions out of the city — Puerto Rico has US-standard signage, your home driving license is valid, but expect aggressive city traffic.