You'll need something called an ARC that stands for an alien resident certificate that will allow you to work in Taiwan for one to possibly three years, depending on the type of ARC that you get. However there are some very distinct disadvantages to having an ARC and the first one that comes to mind is that you will be tied to one employer, which means you can only work for one employer for the duration of your contract.
Of course you can cancel your ARC but then you have to reapply for another one, which is a bit of a pain, and only lets you stay here for one or two years at a time. But what if you want to stay for a really long time like, maybe five to ten or fifteen years?
The first thing that you can do which will allow you to stay here for a very long time will be to work five consecutive years on a regular ARC, so after each one or two years you need to go and reapply until you've been here for five years. Then you can apply for an APRC, which stands for a permanent residence certificate for aliens such as myself.
This is the holy grail of resident certificates because it's an open work permit and it allows you to work pretty much anywhere in Taiwan, and it gives you the same working rights as the locals.
The requirements that you need to prepare to apply for your APRC is a degree, and if you're teaching English it can be in any major or any field. It used to be quite common for a lot of people to just get a fake degree and use that because no one used to check, however the immigration agency caught onto that pretty quickly and they've effectively stamped that out. Now they call the University where you studied and they make sure that you did in fact study there and that you didn't go to Thailand and pick your degree up off the street or something to that effect.
The next thing that you will need is a criminal clearance certificate because if you're coming here to teach English they don't want people with a criminal record coming here to work with kids. I'm very glad that they have that requirement in place because as a father with two kids you sometimes worry. It kind of like gives you a little bit of peace of mind that the people who might be teaching your children don't have a criminal record.
Regarding the criminal record as I recall it has to be done within three months of applying for an APRC. A lot of these documents have a three months expiry day so you have to get all of those documents within three months and successfully complete the application for your APRC within three months. After three months if one of those documents expire then you have to reapply and do the whole process over again. The next thing that you need is a health certificate, which can be done in your home country, however I would suggest doing it here. It's cheap and fast and as I recall it wasn't a very pleasant experience. They took a stool sample, a blood sample, a urine sample and they checked for a whole bunch of different ailments and diseases.
Taiwan Immigration Agency for ARC and APRC requirements:
How to get your APRC in Taiwan:
One-stop portal site: https://www.contacttaiwan.tw