How soon does one have to put up a mezuzah?
As soon as one moves in the same day? within 30 days? or can one do this at any point?
A mezuzah has to be put up as soon as one moves in to a new home.
Outside Israel, if a person is planning to rent a house for less than thirty days, there is no obligation of mezuzah. However, if one is planning on renting for more than thirty days, the obligation is immediate.
Nonetheless, if a person failed to put up the mezuzah right away, he can still do so whenever he can (ASAP), of course with a berachah.