See the introduction to Hungarian possession for a broad description.

First, decide how many objects are owned.

If one item is possessed, remain here.

If several items are possessed you need to check that the number of objects is qualified but not quantified.
That is if we have "some" but you don't know the exact number. If you know the exact number, remain here. If there is no qualification to the plural, go to the page about multiple objects.

Then, select the owner of the object.

The owner is either I, you, he/she/it, we, you (pl), or they.

Finally, apply the relevant endings. Note that for word ending in a vowel you need a linking -j- before the third person single possessive ending.

Owner	Charactistic ending	Endings	Examples
én	-m	-m/om/em/öm	almám	dobozom	kezem	házam	söröm
te	-d	-d/od/ed/öd	almád	dobozod	kezed	házad	söröd
ő	-a	-a/e	almája	doboza	keze	háza	söre
mi	-nk	-nk/unk/ünk	almánk	dobozunk	kezünk	házunk	sörünk
ti	-tok	-atok/otok/etek/ötök	almátok	dobozotok	kezitek	házatok	sörötök
ő(k)*	-juk	-juk/jük	almájuk	dobozuk	kezük	házuk	sörük

alma = apple
doboz = box
kéz = hand, becomes kez- when endings applied
ház = house

Note how alma + aim -->  almaaim --> almáim
See the note on lengthening trailing vowels

Note that it's forbidden to use the pronoun ők when taking of third person plural. Merely ő will suffice. For example ő sörük = ő(k) sörük = their beer.

I leave the (k) in the table to avoid confusion over whether the row represents third person singular owner, or third person plural owner.