Longshan Temple is the most known temple in Taipei. Inside there is a mix of Buddist and Taoist relics. Take 7 insence sticks and bow to the 7 gods present in the temple and your prayers will be heard. I prayed as well - thanks to Charlotte's explanations I found out what to do where in the correct way and order.
The temples themselves are incredible because they survived the Cultural Revolution untouched, hence not only are they in their original state, but also they are incredibly beautiful. Ahh what am I gonna tell you - just take a look yourself.