With over 800 languages, it was pretty difficult to get everyone talking to each other. Two pidgins grew up in this area; Tok Pisin and Hiri Motu, and when the Anglophones married the Hulis and the babies learned the only language they had in common, Tok Pisin became a creole. Tok Pisin sometimes looks like it is English written phonetically ("Yu dring; yu draiv; yu dai" means "You drink; you drive; you die"), but it is not; it has more personal pronouns than English and its own quite different syntax.
Tok Pisin is spoken in most of the country and short, inexpensive guidebooks on learning Tok Pisin can be acquired in the many book stores.
Hiri Motu is spoken in Port Moresby and other parts of Papua, though since Port Moresby is the capital, you're likely to find Tok Pisin speakers in the airport, banks, or government. When approaching locals, try to speak English first; using Tok Pisin or another language can make it look like you are assuming they don't know English.
You might sometimes have trouble hearing what the locals are saying because they speak very quietly. It is considered rude by some of the local groups to look people in the eyes and to speak loudly.