Unicode note. In addition to Western European accented letters ç ö ü (made as ç ö ü) Turkish has special letters that can be made as follows:
Ğ  Ğ   ğ  ğ   G-breve (yumuşak-G)
İ  İ               I dotted capital
            ı  ı   I undotted lowercase
Ş  Ş   ş  ş   S-cedilla
To what follows there are, as with any language, numerous minor exceptions: a full grammar would note them, but my sketch of the system does not need to. A few words, mainly borrowings from Arabic, partly disobey the general principles of Turkish.

Vowel harmony and agglutination

The pervasive features of Turkish grammar are vowel harmony and agglutination. It is actually a fairly easy language at an early level, once the vowel harmony is mastered, and before you get too far into the verbs. The eight vowels pattern neatly into binary features: each one is either front or back, high or low, rounded or unrounded. There are two kinds of suffix: one harmonizes with front or back vowels, for example the plural suffix ler ~ lar. After the front vowels i e ü ö the suffix vowel is e, while after the back vowels ı a u o the suffix vowel is a.
kedi cat      kediler cats        kız girl    kızlar girls
anne mother   anneler mothers     ada island  adalar islands
yüz face      yüzler faces        kuyu well   kuyular wells
köy village   köyler villages     yol road    yollar roads

Other examples of a two-way harmonizing suffix are the locative de ~ da and the ablative den ~ dan: with front vowels yüzde in the face, köyden from the village, Türkiyeden from Turkey; and with back vowels kuyuda in the well, adadan from the island, Ankaradan from Ankara. Agglutination is illustrated by simply combining plural with case endings, with both endings harmonizing: kuyu well, kuyular wells, kuyularda in the wells.

The other kind of vowel harmony is four-way. A suffix uses one of the four vowels i ı ü u depending on whether the previous vowel is front or back, rounded or unrounded (to make that explicit: i after front unrounded i e, or ı after back unrounded ı a, or ü after front rounded ü ö, or u after back rounded u o). One example is the suffix meaning 'is':

kedidir it is a cat        kızdır she is a girl
annedir she is a mother    adadır it is an island
yüzdür it is a face        kuyudur it is a well
köydür it is a village     yoldur it is a road

When a two-way suffix is added, it does not preserve the rounding feature. A suffix harmonizes with the immediately preceding vowel. Therefore a four-way suffix after a two-way suffix is always unrounded: yoldur it is a road but yollardır they are roads, and yüzdür it is a face but yüzlerdir they are faces. Almost every suffix in Turkish, and there are a lot of them, behaves in one of these two harmony patterns. There is a small number that have a fixed vowel, such as the present continuous -yor. Suffixes added to that then harmonize with the o, e.g. içiyor s/he is drinking, içiyorsunuz you are drinking.

Linkage and consonant harmony

Several more phenomena need to be understood from the beginning. They are complications, but are almost always regular. One is voicing assimilation: the voiced stop d in a suffix becomes voiceless t immediately after a voiceless consonant p t k ç f s ş h. So kitap book gives kitapta in the book and kitaptır it is a book, and çocuk child gives çocuktan from the child, and genç young gives gençtir s/he is young.

The second is related to this. As with many languages, you can't get voiced stops b d g c at the end of a word: they become voiceless p t k ç (kitap is from Arabic kitâb). But when a vowel suffix is added, they change to the voiced forms. So with the genitive case ending, we get kitabın of the book and gencin of the young one. With k the change is not to its ordinary voiced equivalent g but the soft (and now silent) ğ, as in çocuğun of the child.

Thirdly, Turkish does not like two vowels to come together, so when a vowel-initial suffix is attached to a vowel-final word, a consonant is interposed. Which one depends on the ending: the genitive in ~ ın ~ ün ~ un takes -n-, as in kuyunun of the well, kedinin of the cat. The dative e ~ a and the accusative i ~ ı ~ ü ~ u take -y-, as in kediye to the cat. The third person possessive is the same as the accusative after a consonant, but has the interposed consonant -s- after a vowel: yolu gördüm I saw the village, yolu her/his/its village, but kuyuyu gördüm I saw the well, kuyusu her/his/its well.

With other suffixes the form after a vowel is shorter than that after a consonant: such as the possessive, -m in kuyum my well and with an extra vowel in çocuğum my child.

Personal endings

There are a number of slightly different sets of personal endings, depending on the use. When the personal pronoun is the possessor of the noun, the following are used (where the vowel i is understood as undergoing four-way harmony, and e two-way).
-(i)m  my           -(i)miz  our
-(i)n  your         -(i)niz  your
-(s)i  her/his/its  -leri  their

Note that the plural form of 'you' is used for the polite singular, as in most European languages. These possessive endings follow the noun plural, so çocuklarım my children, çocuklarımız our children. The third person forms are ambiguous: çocukları can be her/his children or their child or their children (the plural is not repeated).

The personal endings for the present tense of 'be', attached to noun or adjective or adverbial, are:

-(y)im  I am      -(y)iz  we are
-sin  you are     -siniz  you are
-dir  s/he/it is  -dirler  they are

Thus İstanbuldayım I am in İstanbul, genciz we are sick, çocuklarsınız you are children. It is a general principle of Turkish that plurality markers do not need to be repeated: so the houses are in Ankara is just evler Ankaradadır. These endings follow the case and possessor endings: evimdir it is my house, evimdedir it is in my house, evlerimdedir they are in my houses.

These same endings, but lacking the -dir, are used to indicate the subject of a verb in some of the tenses, such as the present tense: geliyor s/he/it is coming, geliyorlar they are coming, geliyorsunuz you are coming; and the future tense: gelecek s/he/it will come, geleceksiniz you will come.

Another set of endings is used with other forms of the verb:

-m  I       -k  we
-n  you     -niz  you
-  s/he/it  -ler  they

One such is the past tense: thus geldi s/he/it came, geldik we came, geldiler they came. Yet other tenses use a different mixture of the two pronoun sets: the aorist tense has gelirik we come but gelirsiniz you come.

Verb inflection

The root of a verb is used as the imperative singular: gel come!, uyu sleep!, yaz write!. As with other second person singulars, this is to intimates or inferiors. The polite singular is gelin and the plural is geliniz.

The aorist or habitual tense has an ending r preceded by a vowel if necessary: gelir s/he/it comes, uyur s/he/it sleeps, yazar s/he/it writes. The personal inflection of this is gelirim, gelirsin, gelir, gelirik, gelirsiniz, gelirler. The choice of the preceding vowel is slightly too complicated for my present sketch grammar.

The continuous present tense has an ending yor preceded by a vowel if necessary: geliyor (s/he/it) is coming, uyuyor is sleeping, yazıyor is writing. The personal inflection of this is geliyorum, geliyorsun, geliyor, geliyoruz, geliyorsunuz, geliyorlar. The preceding vowel is determined by the root, but the -o- never changes, so all verbs have the same personal endings in this tense because of constant vowel harmony on the -o-.

The past tense has an ending of d + four-way vowel, e.g. geldi (s/he/it) came, uyudu slept, yazdı wrote, gördü saw. As with other d-endings, this can assimilate in voicing: baktı looked, gitti went. The personal inflection of this is geldim, geldin, geldi, geldik, geldiniz, geldiler.

The future tense has an ending -ecek ~ acak preceded by the consonant y- if necessary: gelecek (s/he/it) will come, uyuyacak will sleep, yazacak will write, görecek will see. The final -k is subject to the usual change before vowels, so the personal inflections for this tense are geleceğim, geleceksin, gelecek, geleceğiz, geleceksiniz, gelecekler.

The negative is formed with the syllable me ~ ma immediately after the root: imperative gelme don't come!, yazma don't write!; past gelmedi didn't come, yazmadı didn't write. It changes to mi ~ mı before the y of the other two tenses: present gelmiyor isn't coming, yazmıyor isn't writing.

The interrogative is formed with a four-way syllable mi. This follows past tense endings: gitti mi? didn't s/he go?, gördük mü? didn't we see?. But it precedes the present-type endings for first and second persons: geliyor mu is s/he/it coming?, geliyor musunuz are you coming?. When combined with negative: gelmiyor musunuz aren't you coming?.

We can briefly mention numerous other tenses and moods, many of which are formed by combining simpler tense/mood markers: gelmek to come, gelsem if I come, geleyim that I may come, gelseydim if I had come, gelmeliyim I must come, geliyordum I was coming, gelirdim I used to come, geldiydim I had come, gelecektim I was about to come. Yet more affixes form the potential ('can'), evidential ('is supposed to; so I hear'), passive, causative, which can all be combined with the tense/mood paradigms; and also such useful forms as relative clauses and participles.

Adjectives and numerals

Time for something easier. Adjectives are easy. No agreement, no comparison, nuttin'. Given büyük big, we simply say büyük ev big house and daha büyük bigger and en büyük biggest. They can take the personal endings of 'be': büyüküm I am big, büyüktür s/he/it is big.

Numerals are also easy: bir = 1, iki = 2, üç = 3, dört = 4, beş = 5, altı = 6, yedi = 7, sekiz = 8, dokuz = 9, on = 10, yüz = 100, bin = 1000. Compounds are formed by simple juxtaposition: on bir = 11, iki yüz dokuz = 209. The multiples of ten are different words, unanalysable up to fifty: yirmi = 20, otuz = 30, kırk = 40, elli = 50, altmış = 60, yetmiş = 70, seksen = 80, doksan = 90. Other than that they also work by juxtaposition: iki bin yetmiş altı = 2076. The plural ending on nouns is redundant when there is a numeral, so it is not used: üç ev three houses.