Something that might help now already: The suffix for plural in Finnish is -t, so finally something that doesn't come in ten different forms :D Pupu -> puput, kissa -> kissat (cat), koira -> koirat (dog) and so on.
What changes, then, is that some words can't just have the t there without changing something from the middle, e.g. ihminen -> ihmiset (human) - often -nen becomes -set. Trickier is then words with the letter s in them, e.g. vesi -> vedet (water)- and s often becomes d, but that still doesn't mean it's gonna look exactly the same in every word with s, e.g. kausi -> kaudet (season), kuusi -> kuuset (spruce), kuusi -> kuudet (six)...
And another thing is of course how different cases work with the plurals, those have often even more changes to the words themselves, but I think this is enough for now.