Use of Should and Would:
(1) ‘Should’ and ‘Would’ are the Past tense of ‘Shall’ and ‘Will’ respectively. As such they are subject to the same rules as apply to Shall and Will in the Assertive and Interrogative Sentences.
(2) ‘Should’ is used to denote-
(a) Duty or obligation; as, We should respect our teachers. We should take care of our health.
(b) Supposition or possibility; as, Should you meet my brother in the school, give this pen to him.
(c) An improbable action; as, If God Himself should come to his help, he will not be successful.
(d) A purpose, when used after lest; as, Work hard lest you should fail.
(e) A wish, with the first person only; as, I should like to bring it to your notice.
(3) ‘Would’ is used to denote-
(a) A wish; as, Would that I were a minister! (I wish that I were a minister!)
(b) A habit; as, He would go to the gardens on holidays. (He was in the habit of going to the gardens on holidays.)
(c) Obstinacy, persistence or past determination; as, I pushed him hard, but he would not leave his seat (obstinacy). Though the enemy attacked the fort, again and again, the captain would not surrender (Persistence). He would not obey his officer (Past Determination).
(d) A future event referred to in the past; as, He told me that he would be present at the meeting.
(e) A polite request; as, Would you lend me your pen?
(f) An uncertainty or condition; as, If I had worked hard, I would have been successful. If I were you, I would have helped him.