The verbal notion should is expressed in Russian by the short adjective дћлжен, which can be translated by English 'should, ought to, be supposed to'.
Short adjectives are predicatives, i.e. they correspond to 'is/are'. The past tense is formed by adding the past forms of бІть after дћлжен:
Онђ должнђ писђть мђтери. She should (ought to) write her mother.
   She's supposed to write her mother.
Онђ должнђ былђ писђть мђтери. She should have written her mother.
   She was supposed to write her mother.
МІ должнІ бћльше рабћтать. We should work harder (more).
   We're supposed to work harder.
Note that with дћлжен the person involved is in the Nominative case, whereas with the o-form нђдо 'have to, must' the person involved is in the Dative case (as is normal with o-forms, e.g. Мнљ хћлодно 'I'm cold'):
Љй нђдо писђть мђтери. She has to (must) write her mother.
Нђм нђдо бћльше рабћтать. We have to (must) work harder (more).