Why should I put Mezuzos?
Primarily because we are commanded to, as the Passuk in Devarim 6:9 states 'וּכְתַבְתָּם עַל־מְזֻזוֹת בֵּיתֶךָ וּבִשְׁעָרֶיךָ' - 'And write them on the doorposts of your house and upon your gates', this is also repeated later in 11:20. Both of these are read twice daily in the Shema.
In addition, much has been written about the importance of this Mitzvah, the Tur and Shulchan Aruch (YD 285) write that one who is careful with this mitzvah merits a long life for them and their children, and if not G-d forbid the reverse is true. Others (Bach, Aruch Hashulchan Ad Loc) state that a house with a Mezuza has extra divine protection.
A common misconception is that only the main entrance to the home requires a mezuza. Whilst it is better to have one mezuza on the front door than none at all, to properly fulfill the mitzvah (i.e. obligation), every room in the house or office excluding restrooms or bath/shower rooms should have its own mezuza (Rambam Sefer HaMitzvos Mitzvos Aseh 15, Shulchan Aruch YD 285:1, Sefer HaChinuch Mitzvah 423, etc. See Rema, YD 287:2 who calls out this misconception).
All rooms that are more than four cubits long and four cubits wide — approximately 6.5 feet by 6.5 feet (or its equivalent of 37 square feet) are required to have a mezuza — as long as they have a full “doorway” (Shulchan Aruch YD 286:13). A blessing is not recited, however, if the room does not extend at least 6.5 feet in each direction (Shach Ad Loc).
Garages, laundry/utility/boiler rooms, attics (non-trapdoor only), outdoor sheds, and crawl spaces require Mezuzos provided that they comply with the required measurements (approximately 37 square feet) even if they are rarely accessed (Igros Moshe YD 2:141 ). The doorposts themselves must be at least 10 handbreadths high (approximately 32 inches).
Only doorways that have two doorposts and a lintel on top connecting the doorposts require placing Mezuzos with a Beracha. If these conditions do not exist, a competent Rabbi should be consulted to determine whether or not that entryway requires a mezuza; in many cases one should place a Mezuza without a Beracha.
If you own your workplace, Mezuzos must be placed with a Beracha. If you’re working for a non-Jew and renting space from him, a mezuza should be affixed on your office door without a blessing. However, if you are not renting the space, and there is the possibility that your office space could be relocated, then you would be exempt from affixing a mezuza. In Jewish businesses and stores, Mezuzos should be affixed without a blessing.
Where around the doorpost? Slanted or Straight?
The Mezuza is affixed on the right-hand side of the door as you enter the room. Inside the home, in doorways between rooms, this means putting the Mezuza on the right-hand side when facing the room that is more frequently used. If in doubt, consult a competent Rabbi.
The proper place for the Mezuza is at the bottom of the top third of the doorway. In other words, measure the height of the doorway and divide by three; then align the bottom of the Mezuza with the point two-thirds of the way up the doorpost. In most homes, the doorways are approximately 78 inches high, so the bottom of your Mezuza should be no lower than 52 inches from the floor.
Ashkenazim place it at a slight angle, with the top of the Mezuza pointing toward the inside of the room and the bottom pointing toward the outside. Most Sefardim place the Mezuza vertically straight.
Do I have 30 days to put them up?
No, this is actually a common misconception. The Shulchan Aruch (YD 286:22) merely states that one who is renting a dwelling for less than 30 days is not required to put up Mezuzos. When renting for longer than that, or when owning the place you reside (YD 291:3), one is required to put up mezuzot immediately upon moving in.