Cool! I clearly need to learn Finnish
Ok.
Minä (me), sinä (you), hän (him/her), me (us), te (plural you), he (them).
Those are the normal written language ones. You can use them for people or animals. Though if you do use them for animals the wrong context can make you look a bit silly, especially with the plurals (but that's not really different from other languages).
Then there are these, mostly used in spoken language, which you can use for people, animals, or objects, entirely equally:
Tämä/tää (this), tuo/toi (that), se (it), nämä/nää (these), nuo/noi (those), ne (them).
So if there was a horse, a man, a woman, and a tree in front of you, and I said "kato tota" ("look at that", 'tota' deriving from 'tuo/toi'), you'd have absolutely no idea which one I was referring to. Well actually, if I said "kato tota" in any situation without actually pointing at something the same would apply. You can't use it properly without context. Which isn't to say that people don't.
Edit: oh, and just to make it clear, tämä/tää is a regional dialect difference, not a sexual one.
Also, since I apparently suck at parsing, if you refer to yourself/yourselves you have to use the written language one (or a regional version).