Do I need to apply for a visa?

I have a dual citizenship in the US and Taiwan.
I’m going back to Taiwan with my US passport.
It’s my first time going back, so I have no idea whether I need to get a visitor visa, etc.
I’m going back for more than 14 but less than 30 days. What do I need to do so that I will be able to return to the USA?

You should ask the Overseas ROC Representative Office for full details.

For people with Chinese ancestry, Taiwan has different regulations depending on how long you have been overseas, whether you are eligible for military service, what your parents’ nationality is (or was), whether you hold a PRC passport, etc. For people of minority races (whites, blacks, indians, etc.) there are still other regulations.

So, according to the information you have provided here, it is difficult to know your exact situation.