I can add to IcyTea's stuff on Finnish mythology. I’d be happy to answer any questions you might have on Finnish myths and folklore, I'm not an expert, but I've studied the topic a bit. Let me dig up my course notes... *shuffle shuffle*
Tietäjät tietää
To add on tietäjät and their role... the tietäjät (singular ’tietäjä’, come up with something else if that twists your tongue too much) were essentially the wise men/women of the village. These were people you turned to for healing, for dealing with the (restless) dead, finding lost cattle and stolen stuff, turning curses/damages back at the person who caused them, fixing your, uh, bedroom problems, etc. It's mostly very low-key and mundane stuff, but Väinämöinen, the OG bard, does stuff in the Kalevala (Finnish national epic) like singing people into swamps and other badass shit. Songs and singing is generally important to Finnish magic and rituals.
Tietäjät needed to be ’hard of nature’, having a powerful luonto, which maybe means strong-willed and forceful in practice as well. You could tie that into some stat or mechanical aspect. How they accomplished things differed; some went into shamanistic trances, others jumped around wildly in ecstatic inspiration, some did ritualistic stuff. You had subsets and variants: witches and 'trullit' who did harmful stuff, seers, herbalists. Women who’d take care of the bodies of the dead and act as midwives were referred to as 'strong-blooded', though that's not a profession/category per se, more of a quality. Later on Christian priests were there as an alternative - the two existed side by side for centuries to choose from.
The Spirits Grow Restless
Finnish pagan/folklorish ideas of disease and healing generally held that whatever affliction plagued you was the result of a supernatural taint, caused by disturbing/disrespecting the dead or angering the spirits/supernatural beings (’väki’ in Finnish, there's loads of kinds). You could also have lost your soul, been possessed, or been attacked with a noidannuoli (witch’s arrow, some kind of magical projectile), resulting in various ailments. This would be cured by rituals, especially ritual washing, and taking you to the source of the taint to be purified (so to the water if you were thought to be hurt by spirits of the water, the graveyard if the dead, etc).
Generally in magic similarity/connections were important, so you’d use ritual objects like snakeskins, bear paws, belongings of the deceased when dealing with those things.
Bear With Me
The most important being in Finnish paganism is absolutely the bear. Even modern Finnish has countless words for ’bear’ because you could not call it by its true name. The bear had a heavenly/divine origin, so it was a Big Deal. The furs and meat they offered were very important to Finnish communities, so people both feared them and wanted them to return. You couldn’t kill a bear while it was asleep - the soul might not be present, and you want it to be present when killing it.
When bears were killed, there was a whole festival/ritual (’peijaiset’) where people sung to the bear to mollify/deceive it (trying to convince it that it had died in an accident or been killed by foreigners, heh) and someone was chosen to ritually marry the bear. The hunters are also called ’suitors’ and the whole thing framed as a kind of courtship, it’s nifty. There's some evidence that bears and humans were thought to be kin, and could have children with one another. The whole bear would be eaten and the bones returned to the forest to be reused by bears. I like to think a new bear would straight-up reform from them.
So for the love of Ukko, make bears the holy kings of the forest they are, the dragons of the campaign. Bears are already terrifying in real life, so imagine a bear that's divine and supernatural too!
Gods and Beings
I'm not all that well-read on the Finnish gods themselves and there's not all that much concrete information on them. Ukko Ylijumala ('Old Man Overgod') is (possibly) the head honcho, a sky/storm/harvest god, goes around with a hammer, beseeched and used in rituals before battle/hunting/harvest stuff. You might notice the similarities to certain deities in surrounding cultures, whodathunk. He's married to Akka ('Old Woman'), maybe associated with fertility. Women and, uh, their genitalia were generally held to have great power and there's a bunch of rituals I don't think I'm going to describe here. I'm not sure if that's something you'll want to work into your campaign in the year of 2019, but hey, why not.
Other likely-important-but-who-knows gods were Tapio, king of the forest, with his wife Mielikki*, mistress of the forest, and their many daughters; Ahti, god of water/the sea; Väinämöinen, the aforementioned OG bard (but he's also kind of a... culture/folk hero?) and Ilmarinen, master smith (the same deal). The problem is that we don't really know how ancient Finns actually thought of these beings - should we call them spirits or gods or what? For your purposes, it doesn't matter all that much. Perkele was also a god before the word began to mean 'the devil' and then turned into a curse word, so work him in so you can keep shouting Perkele over and over at your table.
Giants and other familiar beings exist in Finnish beliefs just the same. There's a lot of overlap with the myths and folklore of surrounding cultures, plus centuries of later interpretation and modification, and so little point in trying to find some kind of 'pure' mythology. I wouldn't be too worried about mixing and matching a bit.
Googling these things should yield you more information. I'm prolly forgetting some really obvious stuff. Reading a synopsis of the Kalevala could also be worthwhile.
*Isn't Mielikki used as a name for some god in a DnD setting? I can see what they were going for, but the problem is that Mielikki today is a name you'd give to a cow, not a powerful and mighty deity. Oh well...