I think it will be awhile before HIV/AIDS are beaten, the disease mutates so fast any cure will be useless by the time its available to the general public. Basically what HIV does is attack the T cells and inject its DNA into them. The virus DNA (or is it RNA?) goes through a process called reverse transcription where it cuts apart the T cell's DNA and replaces some of it. It uses the T cell's resources, the nutrients from your body and the various parts of the cell to replicate itself then bursts, killing the T cell and releasing more of the virus.
The disease is progressive, it starts out slowly taking out the T cells in your body and continues to replicate slowly. It never makes you sick, your body can't fight it so you don't get sick at all (since illness is really just your body's way of fighting a disease). But it does make you weak against other virii/bacteria. So after the progression of the disease has went far enough you don't have enough T cells to fight any new disease that might come into your body and that will probably kill you.
This does take a long time and there are drugs that help block reverse transcription, slowing down AIDS replication. Its not like you get sick twice then you are dead or something, it could be years and years before you even notice for some people.