Should and would follow the same rules as shall and will in expressions of future time, determination, and willingness. The distinctions between ordinary and formal usage also apply here.
Ordinary: I would like to hear from you.
Formal: I should like to hear from you.
Ordinary: We would be glad to see her.
Formal: We should be glad to see her.
Ordinary: I would be pleased to serve on the committee.
Formal: I should be pleased to serve on the committee.
a. Always use should in all persons to indicate “ought to.”
- I should study tonight.
- You should report his dishonesty to the manager.
- He should pay his debts.
b. Always use would in all persons to indicate customary action.
- Every day I would swim half a mile.
- They would only say, “No comment.”
- She would practice day after day.
c. Use should in all three persons to express a condition in an if clause.
- If I should win the prize, I will share it with you.
- If you should miss the train, please call me collect.
d. Use would in all three persons to express willingness in an if clause.
- If he would apply himself, he could win top honors easily.
- If you would delay your decision, I could offer you more attractive terms.
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Source: The Gregg Reference Manual.