Internet access in South Africa is relatively easy. Most hotels and lodges have some form of access and Wi-Fi is becoming a standard. If not offered, ask your hotel or lodge to connect to their Wi-Fi. There might be a fee for this service.
Various restaurants and coffee shops supply free Internet to their patrons; this is usually advertised on the window front.
South Africa has some paid hotspots, Telkom, Fon and AlwaysOn, as well as a few others, supply these, and they are usually available in airports and shopping malls with a limited amount of complementary data.
When in the rural areas, your only option may be 3G/LTE.
Do not use any open Internet access over Wi-Fi, unless you have a VPN; these are prone to hacking and viruses.