Generally speaking, foreigners are advised to use the international banks to open savings account. You will not be able to use/write checks but will be given an ATM card to withdraw money at will and will earn interest either monthly or bi-yearly on any savings in your account (with tax deducted automatically by the bank- see below.)

Atm machines are located all over Taiwan, and they also accept most major credit cards (as do most stores in Taiwan.) You will be able to withdraw between NT$90-$150,000 from your own bank's Atm daily, and up to NT$60,000 from other bank's Atm's, in general. Personal checks are not widely used or ACCEPTED, and cash is the standard (besides credit cards.)

Opening An Account

Requirements:

1) Passport identification

2) NT$100

You Receive:

Savings account

ATM card

Banks only tax the interest of your savings, and that is at a rate of 20%. They deduct it automatically once a year without any need for you to file any paperwork.
 
English speaking ability is available at most banks (except, perhaps in rural areas...) and the Taiwanese are friendly and helpful to foreigners in general, and clerks are no exception.

BANKING HOURS:  Island-wide banks close at 3:30pm.

CREDIT CARDS:

You'll have to find your best Taiwanese friend to co-sign for you OR have an ARC. Credit cards in general are accepted island-wide at most hotels/restaurants/grocery stores and even smaller establishments.

DIRECT DEPOSIT:

Direct deposit of your paycheck by your school is also available through most banks.