Getting a visa to come to Taiwan is a fairly straightforward process. An easy way is to simply buy a plane ticket from your home country (return/roundtrip) and you will be given a ‘Visa Exempt Entry’ upon arrival at the airport in Taiwan which allows you entry for up to 2 weeks, or for a small fee you can receive a 30 day ‘Landing Visa’ (depending on your country of origin).
These are not the smartest ways to enter as they are a waste of time and money. You will need to leave again in 2 weeks or 30 days since it is illegal to overstay a visa, thus forcing you to fly to a nearby country such as Hong Kong (otherwise known as a ‘Visa Run’) and then return in order to replace your old visa with a new one.

‘Visa Runs' are usually done from Taiwan to Hong Kong. The average round trip cost of the flight is $100.00 USD - $150.00 USD. Since the office is downtown, you will probably need to stay one night at a local hostel and then after all

your paperwork is complete the following day you will return to Taiwan.

If you are planning on teaching, you should apply for a ‘Visitor Visa’ in your home country before you come to Taiwan because you will usually get a longer term visa of (usually 60 days) which will be extendable and you won’t have to worry about spending a lot of time and money coming and going. Plus, if you want to be legal and/or reside in Taiwan for a period of a year or more and are employed in Taiwan (or marry a local) you can apply for a work visa/resident visa from within Taiwan if you have a visitor visa and won't have to return to your home country, although you may have to take a brief 'visa run' to a nearby country and back to satisfy the requirements for application.

You can also study at a Chinese language school, which will provide you with an extendable 2 month visa up to a one year resident visa and you will still be able to work on the side although this is a better idea only if you actually want to study Chinese as you will be required to pay for the schooling and attend on a regular basis.