Cape Town is a town in South Africa.
Towards Bloemfontein, Johannesburg on the N1
Get on a local train towards Wellington and get off in Paarl. A 3rd class ticket is about 10-15 ZAR. From the station just follow the conventiantly named Station Street for about 200 meters until you get to the intersection with Main Street. Turn left and follow Main Street either until you get to one of the 2 petrolstation on the way to the onramp or to the onramp itself. The onramp is the recommended alternative. Thump up and bear in mind that Worchester (which is the last town before the sparsely populated Karoo Desert) is oddly enough pronounced like Wooster. If you pronounce it as a proper Worchester, nobody will understand you.
Towards Port Elizabeth on the N2
To Cape Point
Get on a local train to Simon's Town and get off at the final station. A 3rd class ticket is about 12 ZAR. From the station walk to Boulders Beach and either ask around at the parking spot where there are quite a lot of tourists making a stop to watch penguins en-route to Cape Point or try hitching on the road.
If you wish not to pay the steep 80 ZAR entrance fee to Cape Point you can just get off at the oddly situated roundabout about 200 meters before the tollboth and climb the fence.
From Cape Point it's extremely easy to get a lift back to Cape Town provided that you`re start hitching out before sunset.