One curious note is that in spoken Finnish, the word "hän" is almost never used. It's too formal for us! We use "se" (it) for almost anything; an object, an animal, a person...

Se meni kotiin = He/she/it went home.

Se käski sun oottaa = He/she/it told you to wait.

A Finnish comedian pointed out that often, when we actually use "hän" in spoken language, the meaning can be to disparage the person, to make the person being spoken about seem a bit uppish (almost like using "his highness" or "her highness" to mock someone).

To confuse you further, "puhekieli" is also highly dependant on where you are. It divides into different dialects, with their distinct features, that are spoken but very rarely written. In contrast, you could almost say that "Kirjakieli" is a dialect that is almost never spoken aloud.

Martin gave you a very good answer of some of the most common simplifications, but please bear in mind that the dialects affect the spoken form a lot.

One note about "hevosia > hevosii". This fits the rule, but I myself wouldn't ever say this. It sounds like a young girl's talk to me. I wouldn't say this either most of the time: "vaikea > vaikee". In my talk it is either "vaikea" or "vaikia".

emmä means "en minä"

While kirjakieli is pro-drop (which means it tends to drop the pronouns), puhekieli is more probable to keep using the pronouns.

Kirjak.: En tiedä

Puhek.: emmä tiiä

I once read a list of rules like this, and I'm not sure I still remember them all, but this is what I remember atm:

-The diphthongs in Finnish are combinations of two vowels that end in i

ai oi ui ei äi öi yi

in U

au ou eu äy öy ey

or start in U

uo yö

or 'ie'

All other combinations of two vowels are technically not diphthongs, but just two separate vowels pronounced next to each other. Like ea in vaikea

Puhekieli tends to simplify those groups into one long vowel:

vaikea > vaikee

hevosia > hevosii

-While we're speaking about diphthongs, diphthongs that end in -i tend to drop that i in puhekieli.

kirjoittaa > kirjottaa

iloinen > ilone (final n's tend to be dropped, except when it's a verb in the first person, then the n is crucial to the meaning, so sanon doesn't become sano)

sanoi > sano, which leads to the confusing fact that "se sano" is the past tense of "se sanoo".

If you find anything else about puhekieli confusing, please don't hesitate to contact me. I'm not Finnish, but Finnish grammar is one of the most fascinating things I've looked into, and I know quite a bit about it~