There is an excellent daily service to South Africa. You will fly to either Johannesburg or Cape Town, and then catch an internal flight to Durban International (they go approximately every 2 hours). Your chosen airline will do this for you.
Unlike some European or American airports, international and internal flights operate from the same terminal, so there is no chasing around to another building to catch your conecting flight. Here are some of the major carriers and booking agents all whom will book your flights through to Durban International Airport.
British Airways have a franchaise partnership with Comair who operate a regular internal route network within South Africa. www.britishairways.com
South African Airways operate to all destinations in South Africa www.flysaa.com
Swiss Air will book you through to Durban International - www.swiss.com
KLM Royal Dutch Airlines - www.klm.com
Lufthansa - www.lufthansa.co.uk
Air France - www.airfrance.co.uk
Air Mauritius - www.airmauritius.com
Air Seychelles - www.airseychelles.co.uk