Many people rent homes for the summer, for either a month or two months, and the question often arises as to whether they must affix Mezuzot in the rented homes. The basic Halachic principle relevant to this issue is that one who rents a residence outside Eretz Yisrael is exempt from the obligation of Mezuza for the first thirty days. If he remains for more than thirty days, then he must affix a Mezuza, with a Beracha. Hacham Ovadia Yosef (Halichot Olam, vol. 8, p. 304; listen to audio recording for precise citation) rules that if one knows he will be remaining for more than thirty days, then he may affix the Mezuza even before thirty days have passed, but he would not recite a Beracha. A Beracha is recited only if the Mezuza is affixed after thirty days have passed. Furthermore, if one affixed the Mezuza within thirty days, he does not have to take it down and put it up anew when thirty days have passed.
What makes matters more complicated is the distinction drawn by the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) between a rental with a contract and a rental agreement made without a written contract. The Ben Ish Hai claimed that if a person rents a facility with a written contract for a period of longer than thirty days, then the obligation to affix a Mezuza applies immediately, and a Beracha must be recited. This ruling is very relevant for us today, as the vast majority of rental agreements are made with a written contract. According to the Ben Ish Hai, then, if a person rents a summer home for a period of longer than thirty days, and a contract is signed, he must affix a Mezuza immediately, and recite a Beracha when affixing the Mezuza.
Hacham Ovadia Yosef (ibid.) disagrees with the Ben Ish Hai with regard to the Beracha. He writes that a written contract for a period of longer than thirty days indeed obligates the renter to affix a Mezuza immediately, but a Beracha is not recited. According to Hacham Ovadia, a renter recites a Beracha when affixing a Mezuza only when he places the Mezuza after having lived in the residence for thirty days. In the situation of a written contract, when the obligation takes effect immediately, a Beracha is not recited.
This entire discussion relates specifically to rented residences. One who purchases a residence must affix the Mezuzot immediately when he moves in.
Summary: If a person rents a residence with a written contract, and the rental is for more than thirty days, he must affix Mezuzot immediately when he moves into the residence, but without a Beracha. If the rental is for a period shorter than thirty days, he does not place Mezuzot. If he rents for over thirty days but without a written contract, he is required to affix Mezuzot only after thirty days, and he recites a Beracha. If in such a case he decides to affix Mezuzot before thirty days, he does not recite a Beracha.
