kaplan-meier from a survival function

let assume I have a survival function, given as a solution from a continuous model. To be precise, the cumulative hazard is calculated, Ch(t), and then S(t) = exp(-Ch(t)).
How would you simulate a Kaplan-Meier plot based on this? Here, the so called clinical trial simulation is performed.
My question is, if I understand that correctly, how do you choose the time points to compare S(t) versus uniform random number from [0,1]? The problem is, the more comparisons you do, the higher the chance to simulate an event. I hope this makes sense.
Any comments would be very appreciated,
Cheers, M
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