The Turkish language is a member of the Turkic group of languages, which can be more broadly classified in the Altaic group with Mongolian and other languages. If you want to get even more theoretical, it may be very, very distant cousins with Finnish, sharing the Ural-Altaic language group, and Korean as well. That is somewhat tenuous though, so YMMV.

Characteristics
Like other Altaic languages, Turkish has several notable features. It makes use of vowel harmony, the grouping of certain vowels together when forming words. Its word order is usually SOV, subject-object-verb, but this can be changed for stress purposes. Turkish is an agglutinating language, which means that it attaches its grammatical information to the ends of words, and though complex, it works extremely regularly. Like Finnish, you may run into very long words. One example I found through research was the sentence in English, "Maybe you are one of those whom we were not able to Turkify.." which is represented in Turkish by the word Türkleştiremedigimizlerdensinizdir. Phew! Adjectives always precede nouns. Turkish takes English's lack of grammatical gender to its logical conculsion, the 3rd person pronoun 'o' can refer to he, she, or it. Like Japanese and Korean, Turkish distinguishes topic, but uses word order instead of a particle or agglutination. The topic of a sentence takes initial position, subsequent related information comes before the verb, and peripheral information follows the verb.

Writing
Written Turkish has historically used the Arabic abjad. Since 1928, however, the founder of the country of Turkey Atatürk (Ataturk) promoted the use of a modified Latin alphabet which is now in full use. Spelling is almost entirely phonetic. The alphabet goes as follows (needs Unicode support to show correctly):

A - a
B - b
C - c - Sounds like 'j' in 'jar'
Ç - ç - Sounds like 'ch' in 'chew'
D - d
E - e - Sounds like 'e' in 'yet'
F - f
G - g - Always a hard 'g' as in 'got'. Never soft.
Ğ - ğ - Not exactly a consonant, it rather distinguishes properties of the vowel it follows. When following a member of the 'dark' vowels (a, o, u, ı) it lengthens the vowel, causing it to be held for two beats instead of one. This is not the same as stress, but rather like the difference between 'saw off' and 'soft': the former 'aw' sound is held for twice the time of the latter. When following a member of the 'light' vowels (e, i, ö, ü) it becomes a gliding 'i' sound.
H - h
I - ı - Sounds like something between the 'i' of 'bit' and the 'e' of 'market'.
İ - i - Sounds like 'ee' in 'bee'. Note that the capital of this letter has a dot. I is not the capital version of 'i'. Makes sense, actually.
J - j - Sounds like 's' in 'pleasure'.
K - k
L - l
M - m
N - n
O - o - Sounds like 'oe' in 'hoe'.
Ö - ö - Sounds like 'ir' in 'sir' (Standard American English). It fits almost exactly with the ö of German.
P - p
R - r
S - s
Ş - ş - Sounds like 'sh' in 'sheep'.
T - t
U - u - Sounds like 'oo' in 'soon'.
Ü - ü - Not found in English. Try to say 'eeee' with your lips rounded. It fits almost exactly with the ü of German.
V - v
Y - y
Z - z


Thank you to eliserh and silencio for clarifying information.