Getting around Cape Town is easy. Public transport options around Cape Town include city buses, taxi's, Rikkis, commuter trains and minibuses. The way most South Africans get around is by minibus taxi. They are cheap, efficient and plentiful. You can hail them like you would a cab anywhere in the world. You'll also see Rikkis in the center of Cape Town, they are small brightly colored vans that operate like taxis. Metro Trains run to all the suburban areas and they go as far as Stellenbosch and Paarl in the Winelands. The commuter train out to Simons Town is actually worth taking just for the ride itself. It travels so close to the ocean, passengers sometimes get soaked by the spray.
A fun way to see Cape Town is aboard a "topless" bus (as seen in the photo above). The trip usually last two hours and stops at all the major sights in Cape Town. You can get on and off as you please throughout the day.
To really take advantage of Cape Town's environs, you should rent a car. Renting a car in Cape Town is cheap and the roads are generally in good condition. You can then tour the Winelands at your leisure and explore some of the more remote beaches and coastline.