For getting Matsu, you may have two options. 
1. By air 
Currently Uni Air has flight services from Taipei (TSA) and Taichung (RMQ) Airport. For details, please check UNI AIR website (http://www.uniair.com.tw/). 
2. By ferry 
Shinhwa Navigation runs route "Keelung-Matsu" every day except Tuesday weekly maintenance. For details, check Matsu maritime transportation ticketing system (http://www.matsuebs.com).