Taipei County/Taipei City
Househunting/finding a place to stay.
-Renting a place in Taipei County (Yonghe, Zhonghe, Hsintian, Beitou, Wugu, Linkou, …) usually is much cheaper than renting a place in Taipei City. Wanhua District in Taipei City is rather cheaper too.
-Tsuei Mama is a good option for English teachers.
-You can also check some of the bulletin boards at the Chinese language schools, the English newspapers, the bikefarm and some other places to find more ads.
-One month deposit (sometimes even two months is quite often required).
-Some people come to Taiwan and prefer to stay a few days in a youth hostel and try to find a place while staying there.
-Real estate is of course another piece of cake. You can have a Chinese speaking friend check the yellowpages for you (if you do not have one; otherwise hire somebody to do it for you)
-You could try the financial district (around Xin Yi Road) and the Tienmu area of course.
-There are of course plenty of adds in the Chinese dailies and some specific real estate magazines.
Some general remarks:
-Do you want to ask yourself a few questions?
How long do you want to stay?
How much do you want to pay?
How much comfort do you want to have?
Do you want to share a place or live by yourself?
My 2 cents.