There is no special compute mode. All CUDA-capable cards can perform both computation and 3D rendering tasks “at the same time.” (Really, the card is time-slicing the compute resources between CUDA and rendering tasks. Only one thing happens at a time, but it switches very fast.)
However, in order for a program to make use of CUDA, the program author has to write special code to offload the calculations to the graphics card. So, there is no way to automatically make a program use CUDA. However, some programs have already been updated to use CUDA (and advertise this pretty prominently) so google searching with CUDA + whatever you are interested in might turn up some hits.
In addtion, games which use the newest PhysX drivers now (I think) will automatically offload the physics calculations to the graphics card.