...Helsinki airport to Central Station by bus, train or other public transportation....
Yes, taxi are 40 EUR or more.
Cheapest is public transit:
http://www.visithelsinki.fi/en/come/getting-around-in-helsinki/public-transport-in-helsinki
Public transportation at Helsinki-Vantaa airport and West Terminal
Helsinki Region Transport provides public transport services between
Helsinki Airport and the metropolitan area. In addition, many long
distance buses stop at the airport.
Tram 9 stop next to the West Terminal. Here is a map of tram line near.
the West Terminal.
Note that public transit does NOT have luggage compartments and can be crowded during commute periods. Also multiple stops between HEL and Central Station.
Train service between HEL and the central station just started.
https://www.hsl.fi/en/ringrailline
Ring Rail Line was opened for passenger traffic on 1 July 2015. The
rail line links the Vantaankoski line and main line, providign a new
crosstown rail link in Vantaa. The line also provides a new transport
link from Helsinki city center to Helsinki Airport and the rest of the
country. The rail line is one of the most significant public transport
projects in the region's history.
I and P trains serve all stations along the line. I trains run counter
clockwise (Helsinki-Tikkurila-Airport-Myyrmäki-Helsinki) and P trains
clockwise (Helsinki-Myyrmäki-Airport-Tikkurila-Helsinki). The trains
run every ten minutes Monday to Friday and Saturdays. The journey from
the airport to the Central Railway Station via Tikkurila takes 27
minutes, via Myyrmäki 32 minutes. All trains are modern, low-floor
trains providing easy access for passenger with luggage, prams or
wheelchairs.
Finnair runs coach service between HEL and the Central Station. Finnair coaches have under seat luggage compartments.
https://www.pohjolanliikenne.fi/cs/pl/en/finnair_city_bus_info
Finnair City Bus is the fastest bus service between Helsinki city
centre and Helsinki-Vantaa airport. The fastest route is always chosen
according to traffic conditions. The trip from Helsinki Centre Eliel
square (next to the Central Railway Station) to the airport takes
about 30 minutes. On the way to the airport the bus stops only at
Hesperia park, about 3 minutes after departure. On the way to the city
the bus drives via both terminals and then stops on request at the bus
stops shown on the map. The bus drives via both terminals at the
Helsinki-Vantaa airport on its way to and from the airport.
Enjoy your ride with the free WiFi connection
Tickets can be purchased beforehand online from the Pohjolan Liikenne
online shop. The online ticket fare is 6,20 € one way or 11,40 €
return for adults.