Finnish is an extremely difficult language. Also, to native speakers of Indo-European languages, many of the constructions in Finnish would seem quite foreign and strange. However, Finland is a rather hi-tech country, and thus a lot of native Finnish speakers can be found on the internet. It is from a few Finnish linguists on IRC that I know most of the following:

Finnish is a very, very inflected agglutinative language. There are verb conjugations, for each tense. The personal pronouns are as follows. Note that the personal pronouns themselves inflect, the following are just the common, nominative forms of them.

minä - I
sinä - you (singular)
hän - he/she (no differentiation is made)
me - we
te - you (plural)
he - they (humans)
ne - they (inanimate objects, informally used for humans in some cases)

Verb conjugation in the present tense is actually fairly simple. The personal pronoun is often omitted in Finnish, although in formal or emphasizing situations it is often left in place. Most verbs follow a fairly normal pattern in the present tense. The verb "speak" in it's uninflected form (I'm not entirely sure if calling it the infinitive would be correct) is "puhua", and is conjugated thus:

(minä) puhun - I speak
(sinä) puhut - you speak
(hän) puhuu - he/she speaks
(me) puhumme - we speak
(te) puhutte - you all speak
(he) puhuvat - they speak

The pattern is -n, -t, double the final vowel (such as omista, own, hän omistaa, mene, go, hän menee etc. If the verb already ends with a double vowel, leave it as is), -mme, -tte, -vat. The pattern for the direct past (aka the "perfect" tense) is: puhuin, puhuit, puhui, puhuimme, puhuitte, puhuivat. So as you can see, the endings remain fairly constant.

As is usually the case in any language, the verb "to be" is somewhat irregular, although not quite as bad as you might think. The uninflected form is "olla", and it is conjugated:

(minä) olen - I am
(sinä) olet - you are
(hän) on - he/she is
(me) olemme - we are
(te) olette - you all are
(he) ovat - they are

Verbs in Finnish are negated with the word ei (which also means "no" when spoken by itself) (and, courtesy Loather, does in fact itself conjugate. Oops. I guess that would explain how we can have implicit subjects with negative verbs. I always wondered about that).
Minä en puhu ranskaa - I don't speak French
Hän ei mene asemalle - He isn't going into the station

As for the nouns and adjectives, they have cases much like in Latin. This is what I mean by "Finnish is really hard". In fact, Latin scholars might recognize some of the cases. But Finnish has not five, but fifteen main cases. Here, for the brave souls who wish to know, are the 15 cases, using kirja, book, as an example:

nominative, the basic form. Kirja (book)
genitive, possessive. Kirjan (the book's)
accusative, points to something. Kirja (this book)
partitive, points to something as object... Luen kirjaa (I'm reading the book)
essive, as something... Kirjana (as a book)
translative, refers to change... Sivut muuttuivat kirjaksi (pages bound into a book)
inessive, in something... Kirjassa (in a book)
elative, from something... Kirjasta (from a book)
illative, into something... Kirjaan (into a book)
adessive, on something... kirjalla (on a book)
ablative, from (on top) of something... Kirjalta (from on top of a book)
allative, onto something... Kirjalle (onto a book)
abessive, without something... Kirjatta (without a book)
comitative, Refers to doing something with possessive... Hän tuli kirjoineen (he came with his books)
instructive, by something.. Kirjoin (only in plural)

Prepositions, therefore, don't exist in Finnish. (correction, they do, sort of. But in a different way and purpose than in English) Some things are attached to end of the nouns as suffixes. For example, kirjani is "my book".

The word order in Finnish is more unfixed than English, but some word orders come off as being "normal" and others as being more archaic and poetic. (like "Into the woods I walk" vs. "I walk into the woods" in English). Most sentences do have the Subject-Verb-Object order, however.

One other interesting tidbit. In English, the names of a country and their respective languages are some different, and irregular. I.e., England; English, Japan; Japanese; France; French; Spain, Spanish, and so on. In Finnish, the name of the country and its respepctive language are always the same. The country is capitalized, and the language is all lowercase. For example, the word for Finland in Finnish is Suomi, while the Finnish language is suomi. France is Ranska, French is ranska. England is Englanti, English is englanti.

This guide is hardly comprehensive, and as most of you probably can tell, I'm a native English speaker, so my knowledge of Finnish pretty much consists of what you see here. If anyone who knows more than me has anything to add, I encourage them to add something below or /msg me with corrections.

6/1/01: Yeah, I figured I'd make a few mistakes. Thanks to Lother, vuo, Jope for the corrections. Keep 'em comin', guys. ;) I've ammended my writeup as necessary for said mistakes.