It is very easy to get a Prepaid SIM-card for data and phone calls in Finland and Helsinki. Starting from only 5€.
Where to Buy?

Definitely the best place to buy a prepaid SIM-card in Helsinki is R-Kioski. They offer a good selection of prepaid cards from the 3 biggest mobile phone carriers Elisa, DNA and Telia. You can find their selection in here, information available only in Finnish unfortunately.
You can find R-Kioski in the airport and everywhere in the city. When arriving from an international flight. You can find Alepa on your left side after exiting baggage pick up.
Alepa S-Market K-Market R-Kioski
Plans and Cost
These are example costs and plans for different usage.
Short term stay(week or less):
Telia Prepaid 5,90€
Includes 7€ of balance. 100mb/s internet speed. All SIM-sizes. Data 0.01€/Mb (max 0.99€ day, then no limit).
DNA Unlimited Prepaid 7,90€
Includes 7€ of balance. 300mb/s internet speed. All SIM-sizes. Data cost 0.89€/day unlimited usage
Saunalahti Prepaid 5.90€
Includes 6€ of balance. 100mb/s internet speed. All SIM-sizes. Data Cost 0.066€/MB (max 0.99€/day, then no limit)
Long term stay(more than a week):
DNA Dataprepaid 4G 30 days 24,90€
All SIM-Sizes, 300mb/s speed. 30 days unlimited use.
Telia Prepaid Internet 31 days 24,90€
All SIM-sizes, 100mb/s speed. 31 days unlimited use.
Saunalahti Wifi-egg + 4G 30 days 59,90€
Includes a wifi-egg, best way to share internet for many people. 100mb/s speed. 30 days unlimited use.
Top Up / Recharge
Head to R-Kioski, Alepa, S-Market, K-Market with your phone number and tell the clerk how much you want to top up / recharge and they will do it for you.
WIFI in Helsinki
Free public unlimited WIFI is available in the airport and all around downtown.