Obligation to affix a Mezuzah
If I am purchasing a home, when does my obligation to mount mezuzahs begin?
Purchased homes require mezuzahs, with the blessing, immediately when moving in.
If I am renting a home, when am I obligated to mount the mezuzahs?
You have a 30-day grace-period (outside of Israel only). It is also preferred to wait until after the thirty days (the night of the 31st) before reciting the blessing. Therefore, some authorities, will suggest not affixing any mezuzahs until the 30-day period is up.
Some have the custom to affix all of the mezuzahs immediately upon occupancy, without reciting the blessing. Once the 30-day grace-period has elapsed, one of the mounted mezuzahs (from a room that has a door) should be removed, checked and replaced. That mezuzah may also be replaced with a new or upgraded one. The proper blessing is then recited. Others have the custom of affixing the mezuzahs immediately upon occupancy using tape, and nailing them in on the 31st day. The first mezuzah that is nailed in should be on a room that has a door, and the bracha is recited at that time.
When do I begin counting the 30 days?
You should begin counting from the day you move in, or the day that you begin storing items in the house.