By taxi
Cheap and safe and everywhere. Just don't mind the broken windshields. All taxi fares are negotiated beforehand and will require bargaining. If you're not from Senegal, you will probably have an outrageous price proposed, so check with locals before to get an idea of what they pay, in order to know what you will be able to get. Even if you have negotiated a price, once you arrive your taxi driver will pretend he has no change on him, even if he previously assured you he had.
By bus
The Dakar bus system, known as Dakar Demm Dikk Dakar coming and going, is fairly dependable. Fares are 150 CFA, and there are no transfer. Unfortunately, for newcomers, there's not much in the way of a map of the bus system, so you'll have to figure it out on your own. The number 10 bus runs along the Corniche de l'Ouest and turns into the suburbs at Rue Aime Cesaire. The number 1 bus runs along the VDN.
Cars Rapides. These are the usually blue, yellow or white mini-buses that careen through Dakar and some of Senegal's other cities. There are somewhat fixed rates for certain distances, but you need to check with a Senegalese beforehand. As of 2011 150CFA would cover most destinations. To find out where one is going, flag it down and shout out your destination at the apprenti, the boy in charge of collecting fares who hangs out the back. If she shouts back at you the destination you want, signal it to stop and hop aboard. To stop, bang loudly on the side of the bus, on the roof or signal to the apprenti you want off. Apprenti's don't always speak French, so be prepared to communicate otherwise if you do not speak Wolof.