Parking area meters are everywhere. You walk to a single dispenser of tickets and then return to the car to display them. You can decide the length of your stay and pay according to the zone. Neither the parking areas nor commercial parking is cheap. Parking anywhere else can be expensive - unless is it raining and the LappuLiisat (wardens) stay indoors.
There are also park and ride areas outside the city.
Helsinki city has suffered with more and more cars coming in, and their are moves to either increase the cost of parking or even consider tolls.
At some point in the future the metro will also extend West as it is now formally decided by both Helsinki City and Espoo City. You can't be me, I'm taken