Being told to monitor a frequency, when are you allowed to transmit on that frequency?
First a note on phraseology. In the context of your question, I believe the FAA uses monitor like most of the world uses stand by. I'll be covering the general procedure - if you are in FAA land, replace stand by in my answer with monitor.

If told to monitor a frequency, you are not expected to transmit on that frequency. Monitor is used when a pilot is requested to listen on a frequency to retrieve information from a broadacst. For example, I might tell you to Monitor ATIS 122.750. I then expect you to tune 122.750, listen to the ATIS transmission, and then return back to my frequency afterwards.

If told to stand by on a frequency, you are expected to tune that frequency and wait for air traffic control to contact you there. For example, Standby for Tower on 118.1. When standing by on a frequency, air traffic control is supposed to contact you, not the other way around. However, if you do not get contacted within a reasonable amount of time, you should go ahead and transmit. There is no fixed rule for how long you have to wait - use common sense - just like you would if told to stand by on your current frequency. For example, if you are waiting in line for departure and there are 3 aircraft ahead of you, don't expect the tower to call you before you are next in line for departure. On the other hand, if you are holding short of the runway and there appears to be no other traffic around preventing you from taking off, if the tower hasn't called you within a minute or so, please do try to call them instead. Maybe the controller is busy dealing with other stuff, or maybe they have simply forgotten about you. It does happen, although not often. You could also accidentally have tuned the wrong frequency, and might only realise this when no one replies to a call made by you. It goes without saying that, if you have a safety related message, you transmit it without delay.