You can reach the airport taxis outside of the terminals. Helsinki Airport’s partner taxi operators are Fixutaksi, Taksi Helsinki and Menevä. There are screens in the taxi ranks that indicate company-specific pricing. At the taxi ranks, one lane is reserved for taxis not from the abovementioned companies. With them, you can agree upon the price of the journey yourself.
If you wish to learn more about Finavia airports’ taxi services, the airport-specific websites are the best place to look for information.