I just moved to the US from Johannesburg. I was fortunate enough to get into grad school here so I got a student visa which was all handled by my school.
As for moving over here on a work basis, your best bet seems to be to have a job secured first and then your employer will petition for your visa. In other words, US immigrations want to know you have a job before they will let you in.
Also, the green card lottery (officially named the diversity visa lottery) is a good option, but it can take years to come to fruition. Go to the US embassy website (southafrica.usembassy.gov) and instructions for the application are there (http://southafrica.usembassy.gov/visa_lottery.html). I do not recommend googling the term, as all manner of unscrupulous websites will present themselves!
The long and short is that it really isn't easy at all, but it certainly isn't impossible. Your qualifications will make a difference, as university education is obviously more sought after because you will be a more productive member of the society (in all likelihood).
I'm looking into it as well because my boyfriend is still in Johannesburg, with no immediate prospects of moving here. All I can say is good luck, and if you come right please let me know. Likewise I will share anything new that I learn.