Practically Time experienced on the Moon is the same as Time on Earth (although there are some tiny relativistic differences ;-). Does that answer your question?
Note: Because light takes a finite time to travel (even if very fast) you would notice a very small delay in communications between Earth and the Moon: probably just a little less than a second. As you move away from the Earth this delay increases! Between Earth and Mars a conversation maybe delayed between 8 and 20mins!