You have two options, either fly, or go by road.
Flying to Bocas del Toro
From outside Panama, you fly in to Tocumen International Airport (PTY) in Panama City, Panama. Aeroperlas (Panamanian Domestic Airline) has daily flights leaving from Albrook airfield (ex-US Air Force Base), which is approximately 30 minutes from Tocumen International airport, so be sure to plan for this change of airport when making your flight plans. Flight time from Panama City to the city of Bocas Del Toro is about an hour, or you can fly from Panama City to David to Bocas.
Traveling to Bocas del Toro by Road
Driving from Panama City by car or bus, you take the InterAmerican Highway up to entrance to Gualaca (10 Km/404 Km). Turn up the road to Chiriqui Grande (98 Km) and then, at Punta Peña, the road to Almirante (68 km). Roads are paved, in good condition. Beautiful views in the mountains along the way. From Almirante you need to take a boat (water taxi or ferry) to Bocas del Toro.
Bocas del Toro Touring Guide