MSPS is mega-samples per second. The easiest way to think about this is if you have it continuously generating output codes, you'll get 500MS/s, where each output code is N bits (N being the resolution of the ADC).
As for the number of cycles, that completely depends on the type of ADC. For example, a SAR ADC takes N cycles or so, where N is the number of bits, but it's N cycles of a clock that may be internally generated or asynchronous to your system. The ADC datasheets should have a description of the necessary input clock(s) and start signals.
I hope that helps!