There are no entrance fees to visit Finland's national parks and other state-owned nature reserves. They are free to visit 365 days a year, 24 hours a day.
Open wilderness huts, most campfire sites as well as lean-to shelters in these areas are free to use as well. While free of charge, they are in shared use and you have to be considerate to other users of these facilities.
However, if you wish a rent an entire hut for your party or make sure you have a bed to sleep in a shared-use hut, rental huts and reservable huts are an excellent choice. They are available in some national parks for a fee. You can make a booking and pay online.
Some national parks also have group campsites, which have to booked in advance.
There is no fee to use trails or to collect mushrooms or berries for your own use.