The xe ôm (literally 'hugging vehicle') is a common mode of transport for Vietnamese as well as tourists.
They are widely available and reasonably cheap -- about 10,000 VND for a 10 minute trip, which should get you anywhere within the city center.

Walk the city streets, and every couple of minutes a guy will flag your attention and say "You !! MotoBike?" Longer trips to outlying areas can be negotiated for 25-30,000 VND.

Always agree on the fare before starting your trip. As with most things, a tourist will often be quoted an above-market price initially, and you need to be firm. If quoted anything over 10,000 dong for a short trip, remind the driver that you could take an air-conditioned taxi for 15,000 so forget it. Occasionally drivers will demand more than the negotiated price at the end, so it's best to have exact change handy. Then you can pay the agreed amount and walk away, end of discussion.