It doesn't need to sit at all if you condition the water properly (ie remove chlorine if your water has it and make sure the temperature is correct). To fully cycle a tank you're looking at at least a month to 6 weeks. It will take you 3-4 weeks just for the ammonia to peak before it starts to drop. One or two weeks isn't even 1/2 way there. Try and get yourself some established media from a friend's tank, that's your best bet and the tank will cycle in no time.
The cycle process is done after your ammonia and nitrite spikes are complete and both are back down to zero. The final metabolic waste product- nitrate- must be removed manually with water changes- there is no bacteria that uses nitrate, but nitrate is also not bad for your fish until the concentrations get up over 20-30ppm.
When you have nitrate readings, then you know you are getting close to the end.
Have you considered doing a fishless cycle?