The church holds parish elections, parish being the basic territorial and administrative unit, every four years. All members ages 16 and up (18 and up until just recently) are eligible to vote, and all members ages 18 and up are eligible to run. Each parish elects a parish board, its decision-making body, which is in charge of such things as the budget. The parish boards also elects a parish council, its executive body in charge of such things as hiring most employees, every two years. One person can serve on both the board and the council. A parish council is headed by a priest, though, who's known as a vicar.
Parishes are grouped into nine dioceses, each of which is led by a bishop and has the two additional decision-making bodies of a diocese council (14 laymen, 7 priests, led by a layman) and a cathedral chapter (seven people, including the bishop, the vicar of the parish with a cathedral, and one layman). The chapter appoints parish priests and selects three candidates for vicar elections. All members of a parish ages 16/18 and up are eligible to vote for vicars, and write-in candidates are possible. Apparently a decision to turn vicar elections over to parish councils is on the table, to clear this mess up a bit.
Bishops are elected by a diocese's priests, lecturers (an aging priest-without-the-frills position, I believe) and an equal number of laymen, whom parish boards select from their ranks. Ten voters can nominate a priest to run. A similar process elects the archbishop, the head honcho and general spokesman. The archbishop can only be bishopy to the oldest diocese, but heads the synod, the church's highest decision-making body that decides where the church stands (64 laymen elected by the parishes for four years, 32 priests, the bishops and a few hangers-on like the leader of the military chaplains) and the church government, the executive body (kirkkohallitus, the archbishop, two bishops and nine laymen, one from every diocese and elected by the synod, also known as those feet-dragging bastards at my folks' so clearly they have some say).
Sorry to gab your ear off, but proper answers take time and this was surprisingly interesting. I'm pretty sure I was careful, though I had to translate some of this on the fly and of course don't know how the internal politics work. Larger cities have parish unions, which, have equivalents to boards and councils. This seems rather democratic to my untrained eye. A parish election is actually coming up next month, an archbishop was elected in the summer, and the new bishop of the capital city is a woman. There was an inspiring campaign where she and the other leading candidate, a man, both told people to ignore gender.
How does this compare?