I believe South Africans are eligible for the Green Card lottery. Give that a go, but don't do that while neglecting the more conventional paths.
If you have more than a High School education, are South African and have a job, you are eligible for the lottery.
If you can, while in South Africa, try to get a translation license or certificate. It won't get you in but when the time comes it can be very useful. Yesterday I became a certified Korean - English translator (passed the test, even though I was the only guy who didn't use an electronic dictionary).
The two realistic routes:
1) Find work. This is going to be very tricky.
Let's say you found an employer who really wants to hire you. Both you and the company, through an immigration lawyer, have to provide quite substantial paperwork by March. Here the paperwork is sent into a lottery and is also reviewed and eventually only 20% of all applicants will actually get their H1B work visas. That's 20% of all people who have an employer who really wants them. In other words, even if everything goes right, you have an 80% chance of not making it.
If you do pass the lottery and review, your H1B will be effective starting October 1st of that year. You have to be employed continuously for 5 years on average before you are eligible for applying for a Green Card (Legal Perminant Residence).
If at any point you lose your employment (downsizing, get fired etc.) depending on your citizenship, you may have no grace period where you can find other work. But even if you do have a grace period, the odds of you being able to land another employer who's willing to go through all the paperwork to hire you is very small and odds are it will not happen within the 1 or 2 months the government gives you.
Once you enter the Green Card application phase, your status changes. If you're LPR pending, deporting you becomes a little bit of a challenge for the US government. It takes a few months to go through.
2) Teaching and Nursing.
You apply for school in a US university and get a degree in teaching or nursing which both are occupations in extremely high demand. Nurses don't get an H1B, but an H1C which is a work visa for nurses. Needless to say your employer has to sponsor you and US colleges are also pretty expensive.
When you get your teaching or nursing degree, make sure you find an employer who is willing to sponsor you for your LPR. The road should to an LPR should be shorter after this point but considering the time it takes to get the degree, it can actually be longer than 5 years (if you have no previous college credit that is transferrable to a US college).