Some overlap with stupot's writeup due to historical reasons, but maybe the extra details make this worthwhile...

Finnish uses exactly the same alphabet as Swedish, namely:

English speakers will note that this is looks very familiar, except for the extra vowels ä, ö and å at the end. So, if you have to look up something in a Finnish phone book or dictionary, the order is exactly the same as in English (except that phonebooks do not distinguish between v and w, for reasons explained below).

Now, the actual phonology of the language is a bit more difficult. The following letters are found in native Finnish words:

...with the following caveats:
  • d was added somewhat artificially, some dialects still use t instead
  • g only occurs in the cluster ng, which is actually a single sound, the velar nasal ŋ
The remaining letters
come from various sources:
  • c has been used interchangably with k, but modern Finnish uses it only for loanwords
  • b, f, q, x and z (and g outside ng) are found only in loanwords
  • w has been used interchangably with v, but is only retained in personal names; this is why phonebooks do not distinguish between Virtanen and Wirtanen
  • å is used exclusively for spelling some Swedish names
And courtesy of Gritchka the ever pedantic, a historical footnote: in accordance with the "one phoneme, one grapheme" principle used to systemize modern Finnish spelling, there was a school that thought the sound "sh" (as in shell) should be written as š (s-hacek). However, this sound is only found in a few rare loan words and the combination s + h does not exist in Finnish, so there is no real need for it; the sound is these days almost always written with the two letters "sh".

As for long/short vowels and consonants, the full story is rather complex and too long to be explained here. Finnish orthography really deserves its own node...