If you've booked a stay at one of the jungle lodges Wasai, Sandoval, Posadas, etc your guide will most likely meet you at the airport holding a sign with the lodge's name on it. They will transport you in van to the river Puerto Tambopata to wherever you are going by boat
If you are staying in town, taxis almost outnumber everyone else in Puerto Maldonado, so getting around the town is fairly simple. Motorcycle-driving taxis will take you anywhere you want to go, and the most likely destinations airport - plaza de armas, airport - Puerto Tambopata, or airport - hotel will cost you between 2 - 5 soles about 1 dollar.
If you chose to rent a moped and ride around yourself, feel free. Motorcycle rentals are everywhere in town and normally cost about 5 sol an hour.
