Merhaba. In one of the homeworks I found this sentence:

"Haftasonlari kıtap okumaktan, müzik dinlemekten, gezmekten ve yemek yapmaktan hoşlanıyorum."

I imagine this means "During weekends, I like reading a book, listening to music and going for a walk.", but I don´t understand what tense the verbs like yapmaktan or okumaktan are in. What is the (mak)tan/(mek)ten in the end? - I´m not even sure which one is the suffix!

They dont have tenses. They are in their infinitive forms like "to do", "to go", "to see". But sometimes you prefer to make them gerunds adding ing suffix to them when you use them as objects or subjects in English. Ex: going, walking, seeing. Adding mek/mak suffix to verb is one of the ways to make a verb object or subject in Turkish. But that is not enough. Verbs also want objects to be direct or indirect. So you should add other suffixes too.  Hoşlanmak always wants objects to be in ablative form. That means it wants them to be indirect. So we should add this -den/dan suffix. The equivelant of this suffix is "from." in English.

1)"Yürümekten hoşlanıyorum" can be translated as "I like walking".

2) But it can be translated like this too "I take pleasure from walking".

So Turkish sentence is similar with the second example.

I made some editing and added extra information to my post.

-mek/-mak is the infinitive suffix. That´s to say, the name of the verb.

yap- (do)

yapmak (to do)

Bir şey yapmak istemiyorum. (I don´t want to do anything.)

The verb "hoşlanmak (to like, to get zest, to get enjoy)" is used with the ablative case.

Hayvanlardan hoşlanmam. (I don´t like the animals. (purely: I don´t get zest from the animals.)) -dan : ablative

Yemek yapmaktan çok hoşlanırım. (I like cooking very much. (purely: I get enjoy from to cook very much.)) -tan: ablative

Doğru yazım (correct orthography) :

Hafta sonları kitap okumaktan, müzik dinlemekten, gezmekten ve yemek yapmaktan hoşlanıyorum. (purely: On the weekends, I´m getting enjoy from to read book, to listen to music, to stroll and to do a meal) (normally: I like reading book, listening to music, strolling and cooking on the weekends.)

http://www.turkishclass.com/turkish_lesson_323

http://www.turkishclass.com/turkish_lesson_257

http://www.turkishclass.com/turkish_lesson_305

Very well explained, both of you. Teşekkür ederim!