Conjugasion:
verb stem + -아/어/여 + -야 되다/하다
Les exemples:
자 + -아/어/여 + -야 되다/하다→ 자 + -아 + -야 되다/하다(-아 is chosen because 자 ends with a vowel.)→ 자야 되다/하다 [ja-ya doe-da/ha-da]
(Drop the -아 because it is the same as ㅏ.)→ 자야 되다 and 자야 하다 are the same things.
쓰 + -아/어/여 + -야 되다/하다→ 쓰 + -어 + -야 되다/하다
(-어 is chosen because 쓰 does not end in ㅏ or ㅗ.)
→ 써야 되다/하다 [sseo-ya doe-da/ha-da] (쓰 + 어 together change to 써) → 써야 되다 and 써야 하다 mean the same thing.
However, it is more important to understand WHY -아/어/여야 되다/하다 means “to have to” or“should”.