"Mezuzah" is a Hebrew word meaning doorpost. It actually refers to the parchment tightly rolled into a case that is placed on doorways of Jewish homes. The parchment is inscribed on one side with the Hebrew prayer "Shema" that is a proclamation of G-d's Oneness. Sha-dai, a name of G-d, is also inscribed on the other side of the parchment. Sha-dai is an acronym for "Shomer Daltot Yisrael", meaning, "Guardian of the doorways of Israel".
Jewish people will often touch the Mezuzah when passing through a doorway and then kiss the fingertips of the hand that touched the Mezuzah. This custom of kissing the Mezuzah demonstrates love and respect for that which is written inside.
The book of Deuteronomy (6:9, 11:20) states;
"And you shall write them on the doorposts of your house and on your gates".
The Jewish Sages understood from this phrase the need to hang Mezuzot on doorways. This is a way of taking Judaism out of the Synagogues and learning halls and bringing it to each and every Jewish home. The Mezuzah serves as a constant, daily reminder of G-d's presence in our lives.
Upon moving into a new house, one should immediately affix Mezuzot. In the case of a rented house or apartment, one is obligated within thirty days to affix a Mezuzah. In the case of Israel, even in rented homes one must affix a Mezuzah immediately due to the commandment of living in the Land of Israel.
Check how many doorposts there are in the house, barring those of bathrooms and spaces less than 6.5 by 6.5 feet. Mezuzot aren't hung on doorways of bathrooms or on doorways of places that are too small to be considered a room. The amount of doorways counted is the amount of Mezuzot you'll need to buy.
Mezuzot can be bought from any reliable source. Reputable local and online Judaica stores will often have a wide range of Mezuzot available. Be sure to clarify what you are purchasing; an empty or already-full-and-ready-to-use Mezuzah. One should be aware that in order to fulfil the obligation, the Mezuzah must be hand-written by a specially qualified scribe on special parchment with special ink. If one buys the cases and scrolls separately, one must roll the scroll from left to right and place it right-side-up in the case.
If the cases have holes at either end you'll need nails and a hammer in order to fix them to the doorways. If not, strong double-sided can be used.
One should place the Mezuzah on the right-hand doorpost (from the perspective of a person entering the room) at the bottom of the upper one-third of the doorpost. The top of the Mezuzah should be slightly tilted towards the room.
Before nailing or sticking the Mezuzah in place, the following blessing should be recited,
"Blessed are You L-rd our G-d, King of the universe, who has sanctified us with His commandments and commanded us to affix a mezuzah".