The first thing to do is to make certain you're eligible to vote. If you've received a letter in the post detailing your polling place, then you're on the electoral register and you'll be able to vote.
If you haven't seen that paper, then you need to check. You can call your municipality's 'keskusvaalilautakunta' (central election committee) to ask if you are on the electoral rolls, and if so, where you should go to cast your ballot.
Finland uses the d'Hondt electoral method, in which each party fields a list of candidates and voters can pick which of the candidates they support. The party's total votes are then tallied and the places on the local council distributed proportionate to each party's level of support. Each party's places are then allocated in order according to the level of support each candidate received until all the party's places on the council are allocated.
To find a candidate you want to vote for, you can look at their election campaign material, website and/or social media presence, read as much as you can about the election, try to meet candidates in person at their stalls in public places or even try one of the Finnish-language 'election machines' available online. You can find a list of candidates at vaalit.fi.
Coffee and democracy
To vote on election day, 9 April, you must go to the polling station at which you're registered and take valid ID. That can be a passport, police-issued ID card, driving license or Kela card with a photo.
If voting in advance (29 March-4 April), you can do so from any advance voting station in your municipality. These are typically town halls, libraries and post offices. You can find a list of those polling places from the vaalit.fi website.
Once at the polling station, you'll show your ID and get a ballot paper from the clerk. Go to a polling booth, write the number of the candidate you want to vote for in the circle, and fold it over. Don't write anything else or make any other markings on your ballot paper, as these could invalidate your vote.
Now head to the polling clerk next to the ballot box. He or she will stamp your folded ballot paper and show you where to place it in the ballot box.
Now you're done, you've exercised your franchise and had an impact on municipal politics. If voting on election day itself, rather than in advance, there may well be a stall outside the polling station selling 'election coffees' with the proceeds going to a good cause—you can join in by having a drink and a snack to celebrate Finnish democracy.