How can i go to Taiwan Lantern Festival in Taoyuan 2016?

The festival will be held at the square of Taoyuan High-speed Train Station from Feb.22 to Mar.6.
So from Taoyuan Airport, take bus no.705 to get to there directly. The ticket fare is NT$30 per person. It takes around 15 to 25 mins on the way.

Thank you for your great detailed answer.
I am so sorry that the question i asked you was incomplete to my plan.
Since I have planned to go there from Taipei Main Station. Do I have to go there only by THSR? I found that the fare is rather cost. If my 3 friends and I take taxi aroud 10 pm until after midnight, the cost will be cheaper or more expensive than take THSR from Taipei Main.

Well, actually, Taipei Main Railway Station and High-speed Train Railway Station are in the same building but different floors. So you can just walk out of the building and arrive at the front square.

Wow! Thank you so much. You are very nice. I appreciate your kindness.