what are the best options to get from the airport to downtown. thanks
Does your BEST OPTION mean the cheapest way???
If so, you take Kuo-Kuang Motor Transport from airport to the city. It costs you TWD125 (about USD4) only.

thanks. is there also a train? my flight gets in at 7pm and i would still like to get out and see the city that nite.
There is no train direct to the airport. The bus usually takes around 50 minutes so you will still have time to look around once you get to Taipei.
It is worth noting there are several bus companies and they go to different points in the city. If you have the address of your hotel check which one will drop you off closest to it.

Here are your options.
1) Taxi. It will cost you about $40-45 US (paid in Taiwan dollars - I'm too lazy to look up the current exchange value) this way.
2) You can take a bus which is really cheap, BUT what nobody will tell you is that this is more difficult than it seems. Buses are rarely on time and drivers rarely speak English, but if you can figure out where to catch the bus and get on the right bus, you'll be fine. In my limited experience buses have electronic signs and maps in English.
3) This is not your quickest or cheapest option, but it is another possibility that is cheaper (but slower) than going by taxi. It's not as fast or cheap as a bus. Take a taxi to Taoyuan High Speed Rail (HSR) station. That will cost you the equivalent of about $10 US. From Taoyuan HSR take the HSR train to Taipei Main Station. I don't remember the price, but it's not expensive - should be less than $10 US. From Taipei Main Station you can go wherever you want by metro (MRT).
The KuoKuang Bus leaves every 15~20 mins and is pretty good -NTS125/-. No worries on their timing as they have plenty of buses. From Taipei Main Station Exit 3 where you alight, many cabs there to take you to your Hotel. You should be in your Hotel by 8.30
You can go to the 101 bldg [if it is a clear night ] for a view of the city from their Observatory -NTD400/- till 10.30pm.If you are still not tired, you can visit the Shilin night Market-Jiantan MRT stop.That closes about 1am or so.
Edited by: nuttyazn

OK I'm going to disagree with jman.
The signs to the bus stop at the airport are all in English. It is so easy to find. The people at the information counters in the airport do speak English, though not fluently, but well enough for your purposes. If you are really worried you can get them to write down "Taipei Main Station" for you (or wherever you want to go - grab a map or guidebook to get ideas) in Chinese.
Guo-guang's bus is the best, most direct, most on-time way to get into the city. They are not usually 'late' as the buses come frequently enough that no matter what you won't be waiting more than 10-20 minutes for one (I usually wait about 5 minutes). It is easy to find as the ticket counter says "KUO KUANG" on it in English.
Once you buy your ticket (the clerks do not speak English but even if you go up to them and say "Taipei MAIN STATION", they will understand you. They deal with this all the time. Chances are overwhelming that someone in the bus stop area speaks English as it is an international airport.
Once you have your ticket, the people outside will help direct you to your bus. People are very friendly in Taiwan - if they can't speak your language they will go out of their way to find someone who can.
Once on that bus, Taipei Main Station is the last stop, plus it's the really dense area with the huge train station right there, where most people get off. You can't miss it. Plus if you look enough like a confused foreigner somebody will say to you in English, "This is Taipei Main Station", or the bus driver will get your attention with hand gestures.
So don't worry about it.

I should note that if my fiance's parents, who are in their 60s, don't speak a word of Chinese and have only been to Asia once before (to Korea) could figure out the bus to Taipei from the airport, so can you.

Agree with Channa about the buses... I usually don't even have to wait to get on a bus once I've bought my ticket.
Taiwan is full of people competent in English; younger people in large cities especially can speak at least basic English. Moreover, Taiwanese people are often compulsively helpful. You will not have trouble finding someone in the airport to help you- if you look lost and confused enough, someone will probably approach you.
Frankly it is beyond me why you would want to take a bus to the HSR station and then take the HSR to Taipei, unless you're dying to take the HSR- it is more confusing than just taking the bus straight to Taipei and more expensive, not necessarily more comfortable, and will not save you a huge amount of time (20 mins on the HSR, not including taxi to HSR station and possibly waiting for train; vs. what has never been over an hour on the bus in over the dozen or so times I've taken it).