Hungarian possesion is very alien to the Englishman.

The biggest difference is that the possessed object is modified, not the possessor. That is, the object owned is changed, not the owner.

könyv = book
Daniel könyve = Daniel's book

The endings that attach to the possessed object are very similar to those for the definite conjugation, I'm not sure whether this is by chance or not.

The endings differ depending on whether one item is possessed or many items are possessed.

There is a unique way of expressing ownership, and of external possession.

There are two ways of expressing ownership. One is common, the second stresses the owner, or is used in complex daisy-chained statements of ownership.

The first:
Daniel kutyája. Daniel's dog.

The second, we use the dative case dative, and the article. Do not forget the article when you use the dative for ownership!

Danielnak a kutyaja. Daniel's dog.

Daisey-chained statements of ownership:
láb = leg
lába = his leg
kutya lába = (the) dog's leg.
Danielnak a kutyájának a lába = Daniel's dog's leg.
Danielnak a kutyája lába = Daniel's dog's leg.
Daniel kutyájának a lába = Daniel's dog's leg.