A taxi to yourself is called a 'course' and will cost about CFA2000 or CFA5000 per hour. A good private driver with a reliable car is Alex Binga.
One seat ('une place') in a shared taxi around town costs CFA300–500. Make sure you are on the correct side of the road for your destination. When you hail a taxi, tell the driver where you're going and how much you're prepared to pay for 'une place'. If he doesn't know the destination or doesn't like your price, he'll simply drive off without a word. Street names are rarely used by taxi drivers, so it's better to know a significant roundabout or a prominent building such as the Presidential Palace or main post office, close to your destination. Libreville suffers from significant traffic congestion, so you'll need some patience.