Submitting your tax returns as a foreign resident in Taiwan couldn't be simpler. If you lived in Taiwan more than 183 days of the previous year, you will need to file taxes. This is done from May 1st to May 31st of each year. While most internationals choose to go the local tax office to file taxes, you can also do it online. Going to the local office is very convenient as they do taxes for foreigners in several minutes through a dedicated desk. Don't forget to bring along your ARC as proof of identification (although you may be asked for your passport, the ARC alone should suffice), and take your NIH card as it makes deductions for itemized medical expenses trivial (as those are all recorded by the same system). If you get a tax return, they will deposit this directly into your bank account approximately three months after you file your taxes. If you owe the government money, then you can pay on the spot; typically the amount owed will be a few 10,000 NTD, so plan accordingly. The full information on how to file your taxes is given here, and more information can be found here.
Academia Sinica policy mandates that if you spent 183 days the previous year in Taiwan, 18% of your income will be withheld for the entire duration of the following year. You will get a substantial portion of this amount returned to you (approximately NTD 122,000 for the typical postdoc) when you file your taxes the following year.