To move around Ho Chi Minh City I recommend the taxis. They are quite inexpensive here. before telling the taxi driver where you want to go, ask him how much is the charge per kilometer -- in Saigon there is no time fare, the price depends only on the distance. If you do not trust the driver, bring a map and try to figure out if he is following a logical route.
For the solo travelers, there is another option to move around, the motorbike taxi. It won't be difficult to spot them, they are everywhere in Saigon. In the center of the city, they will offer their services all the time. This is the fastest and cheapest way to move around. For security reasons, do not take motorbike taxis in places you do not know, specially during the night.