I don't use CFD for aerodynamics, but I do use it for other applications with turbulence.
Modelling turbulence and flow separation is all really a question of scale. If you want a precise model of what each particle is doing within the flow then you will need a super super computer, a microscale model and a very very long time-even with today's computers.
However, if you are interested in so called 'averaged quantities' e.g. lift, drag, pressure field etc. then current CFD software is eminantly capable of doing the job. Flow separation will be adequately predicted and lift/drag should be predictable to within a percent or so.
The basic starting point for all CFD models are the Navier-Stokes equations which predict the flow of a fluid with viscosity. For turbulence, the most common approaches at the moment use the so-called two-equation models (k-omega model or k-epsilon model). Which of these models to choose is far from straightforward and is not something that the amateur can or should do.
There are other turbulence models coming along at the moment-some are better proven than others.
If you put some of the keywords above into Google or Wikipedia it should be easy to find some more information. Another good source of information (if you can get it online) are the ERCOFTAC Best Practice Guidelines which have several examples of turbulence and flow separation modelling. ERCOFTAC is the European Research Community on Fluid Flow, Turbulence and Combustion.
Hope that helps. If you're still awake feel free to pm me if you want to know more.
Bri