diye - that, so that, in order to

Çalışsın diye yeni bir kitap aldım.
I bought a new book so that he studies.

We use the imperative form (command) of the word and the word diye after it.
There is another way of telling the same sentence in Turkish.

Çalışması için yeni bir kitap aldım.
I bought a new book for him to study.

These two Turkish sentences mean exactly the same.
In the second sentence we used a different grammar.

onun çalışması
this is a normal genitive phrase but we usually skip the pronouns.
for example; onun annesi -> annesi (her mother)
here we make the verb çalışmak a noun first. "çalışma" , and then we form genitive.
This form with "için" something that you can see in formal and written language more but it does not mean it is something we never use in spoken language; we do use it. But about "diye", it really is seen in daily language more often than "için".

Let's see more examples.
Sen de gel diye aradım. I called so that you also come.
Senin de gelmen için aradım.

Now I used the personal pronoun, cause we used the word "also" with it.

When we use için, the grammar has some rules maybe you haven't studied yet, but actually there is a simple formula.
1) take your verb in -mek form
2) delete the k
3) add the necessary genitive suffix

it is the same thing with saying benim annem, senin annen
benim gelmem, senin gelmen, onun gelmesi, bizim gelmemiz, sizin gelmeniz, onların gelmeleri/gelmesi
This is the case for present tense.

There is a second use of "diye" which tells about the reason;
you just use the normal tense and add the word "diye", it is that simple.
Ben gelirim diye bir sürü yemek yapmış.
She made so much food thinking I will come.

Okula gitmedim diye annem bana kızdı.
My mother got angry at me as I did not go to the school.

Onlar gitmeyecek diye biz de mi evde duracağız?
Will we also stay at home as they will not go?

Seni dün aramadım diye mi konuşmuyorsun benimle?
You are not talking to me because I did not call you yesterday?

and here is a trick for you;
if you start your question with the word "sırf" first, it adds the meaning  "just"
Sırf seni dün aramadım diye mi konuşmuyorsun benimle?
You are not talking to me just because I did not call you yesterday?

The third use is about the spelling.
diye okunmak : to spell
How do you spell this? Bu nasıl okunur?/söylenir? Bunu nasıl okursunuz?/söylersiniz?
Güzel diye okunur.

And the fourth use is saying what something is called
Seni Ali diye biri aradı. Someone who is called Ali called you.
Yonca diye ünlü bir marka bu, duymadın mı? This is a new brand which is called Yonca, haven't you heard?

There can be more uses as well, but these are the ones right now I could think of. I hope you've found it helpful.