Must, Have to, Need to, Want to
1. Must
The best counterpart in Turkish for the meaning of necessity that is given with 'must' in English is the suffix '-meli'. The skeleton for using a verb with this suffix is as follows:
verb-meli-to be

I must go --> git-meli-im --> gitmeliyim (note the use of the fusion consonant y)
We must study --> çalışmalıyız (note that the suffix -meli becomes -malı due to the major vowel harmony)
You must sit down (plural) --> oturmalısınız
You must go home now. --> Şimdi eve gitmelisin.

We can show how to express the necessity of a verb the for different cases of person:
Personal Pronoun
Suffix
Ben -meliyim
Sen
-melisin
O -meli
Biz -meliyiz
Siz -melisiniz
Onlar -meliler

2. Have to
The meaning of formal obligation that 'have to' gives in English is best given by the word 'lazım' in Turkish. The structure for using this construct is as follows:
verb-me-possession (blank space) lazım
This might seem confusing, let us explain how this structure works. The suffix -me allows a verb to be used like a noun, it is similar to a gerund. You might ask at this point, wasn't the suffix -me used for negating verbs? That is right, but the suffix for negating verbs and the suffix for using a verb like a noun are the same. So, okuma can mean either don't read or reading according to the context in which it is used. In this case, we are concerned about the second meaning. So, in the phrase okumam lazım, the part okumam means my reading and the part lazım means required. When we put these together, it becomes my reading is required and this is what we use for I have to read in Turkish. Let's look at a few examples to clarify this further:
I have to go to school tomorrow. --> Yarın okula gitmem lazım.
I have to work now. --> Şimdi çalışmam lazım.
We have to get ready. --> Hazırlanmamız lazım.
You have to go. --> Gitmen lazım.

3. Need to
This is very similar to the use of have to, both in meaning and structure. The word we use to give the meaning of need to is 'gerekiyor'. It is similar to 'have to' in meaning, so that it can be used interchangeably with have to (lazım). It is similar in structure, which can be seen in the structural skeleton:
verb-me-posession (blank space) gerekiyor
The following examples will clarify this further:
I need to go home. --> Eve gitmem gerekiyor.
You need to be here at 2. --> Saat ikide burada olman gerekiyor.
You need to sleep early. --> Erken uyuman gerekiyor.
She needs to see a doctor. --> Doktora gitmesi gerekiyor.

4. Want to
The use of want to is logically almost identical to the English counterpart. One important difference is that you use the verb 'to want' in present continuous tense instead of present simple. The turkish verb for to want is istemek. The structure goes as follows:
verb(infinitive) (blank space) istiyor-to be
I want to go. --> Gitmek istiyorum.
I want to sleep. --> Uyumak istiyorum.
I want to take a rest. --> Dinlenmek istiyorum.
I want to go home. --> Eve gitmek istiyorum.
What do you want? --> Ne istiyorsun?
Konuşmak istiyor musun? --> Do you want to talk?