Buy bitcoin in South Africa from a bitcoin exchange
The two oldest exchanges in South Africa for buying bitcoin, are ice3X (iceCUBED), and Luno. Both of these bitcoin exchanges will accept a deposit from your bank account, and once the funds have cleared, you can purchase and trade bitcoins. Buying bitcoin from an exchange is the safest and most secure way to buy bitcoin when you are starting out.
Luno exchange currently only offers customers bitcoin and Ethereum (Step by step instructions on how to use Luno). Luno also has an App for mobile trading, which you can download here: Android / Apple
Ice Cubed exchange also allows its users to buy and trade in bitcoin and a wide variety of other cryptocurrencies, with altcoins such as Ethereum, Litecoin, Dogecoin, Zcash, Bitcoin Cash, Neo, Monero, Ada and Dash. (Step by step instructions on how to use ice cubed) IceCUBED also have an App for Android which you can download here: Android