You can fly in on one of Peru's national airlines (which are often going in and out of business) - Star Peru or LAN, a more stable South American airline. LAN is more reliable as far as timing and service, but only offers a 5 am flight. StarPeru is currently the only airline that offers daytime flights to and from Pucallpa (mid morning, and early evening, assuming that the flights are on time). Also, LAN has drastically different fares for Peruvian residents, and visitors can't get the reduced fares (which require a Peruvian ID). StarPeru's fares, on the other hand, are the same for nationals and guests. You can book flights directly through the airlines, or you can use a Pucallpa-based travel agent, like Amazon World (011-51-61-57-5539). The advantage to using a travel agent (my only experience is with Amazon World) is that if a flight is delayed or canceled, they will go out of their way to notify you, or even to make arrangements if a cancellation causes you to miss another flight.
Its possible to travel by boat south from Iquitos on the Rio Ucayali all year round and possibly north from Puerto Bermudez or other ports along the Rio Pachitea depending on the time of year and river height. It's also possible to come from the south, nearly all the way from Cusco by smaller boats along the Urubamba and Ucayali river.
Buses from Lima take about 18 hours or more (about S/.50 - S/.100; "Transmar" and other companies). Be aware that there a twi streets called 28 de Julio in Lima. One in central Lima (there is Transmar) and one in Miaflores (no Transmar there).
The road past Huanuco is very foggy at times, with little visibility. Past Tingo Maria landslides have devastated the road in sections, you can get through but its muddy and slow going in small sections.
Mototaxis are motor-tricycle taxis that are the standard mode of transportation for Pucallpa. Expect to pay about S/.2.00 for a trip within downtown, S/.3.00 for a trip in from the outskirts of town, and as much as S/.6.00 for a trip from one of the suburbs (you might need to switch mototaxis). About S./4.00 to Yarinacocha.
Collectivos are normal passenger cars that run set routes (like buses). They are a cheaper option for travel (especially if you are alone - S/.1.00 per person). Note that the collectivos can get crowded - two people in the front seat and four across the back seat. Pucallpa to Yarinacocha is S./1.50.
On Foot: Downtown Pucallpa is small enough that you can get to many places just by walking. If you don't know where something is located, ask directions, but be aware that the directions you are given are not guaranteed to be correct. People feel compelled to give an informative answer, regardless of whether or not they know the right one.
There is not very much in the way of sightseeing in Pucallpa itself. That said, most attractions are water related. Pucallpa is situated on the shores of the Ucayali River, and there is a lake near the city called Lake Yarinacocha. In the middle of the lake is an island called La Isla de Amor. This is a nice place for a day trip.
If you need a very good english speaking guide for showing you around, see Richard, a local guy who is in local shipibo artscraft and guidance. He is trustworthy, and knows almost every interesting place in and around Pucallpa. If you like his services pay him a breakfast or a little fee. Call him: 961692118
There are a number of markets within Pucallpa. These markets are filled with booths that are manned by vendors selling all sorts of wares. Hammocks are best bought at the market nearest to the Ucayalli River (Mercado numero 3), and you can buy any number of artifacts/crafts from many of the surrounding indigenous tribes. There are also pharmacies, banks, travel agencies, and 3 grocery stores with imported projects. Los Andes market is a delight for anyone looking for European or North American products. Fisa is the smallest of the three, but carries some Asian products that can't be found elsewhere. Valdivia (Near the plaza de Armas) is your best bet for many other imports, and has a wide selection of liquors and wines. If you are looking for a specific product, and have some time on your hands, you can ask the proprietor of the store to order it for you. You can get inexpensive, custom made furniture from a place in town called "El Huecito".
There are many cheap hostels around the Plaza de Armas, ranging from about S/.10.00 per bed.
The road between Tingo Maria and Pucallpa is infamous for robberies. Particularly buses are prone to suffer, as some of the robbers get on as paying passengers and then stop the bus while more robbers get on and strip the passengers of all valuables. It is much safer to use a plane from Lima. If you have to use the road, try organizing a taxi or lorry from Huanuco. Avoid travelling when there are special events in Pucallpa (or Christmastime), as the robbers are known to be more active then. And don't ever travel this road at night. Pucallpa is particularly dangerous around Christmastime. Many robberies occur during December, and police corruption is at its worst then, too. The situation seems to have improved since the road between Tingo Maria and Pucallpa is mostly paved now (as of 2011).