Transit flight process

Transit flight process?
I've never traveled internationally by myself and I was wondering what's the procedure for transfer flights? I'm flying from Honolulu, Hawaii to Chiang Mai, Thailand with 2 stopovers in Tokyo and Taipei (China Airlines). The 1st stopover, there's no plane change, so I'm not worried about that one, but my stopover in Taipei is an overnight layover. My flight from Taipei to Chiang Mai is with Mandarin Airlines, which is a subsidiary of China Airlines. My question is do I have to check in with Mandarin Airlines or do I have to go through some kind of check-in process at the transit area in the Taipei airport?
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Shannon, the agent at Honolulu will tell you where you need to check in again and will answer any questions that you have. Probably(!) you will have to check in with Mandarin in Taipei. Regards, Dan