The use of should and would is in general the same as that of shall and will in indirect statement.

Futurity
I should We would
You would You should
He would They should

In asking questions use should in the first person to express mere futurity and would to express volition, etc; in the second and third persons use the form that is expected in the answer.

Futurity
Should I(I should) Should we(We should)
Should You(I should) Should You(We should)
Would he(He would) Would they(They would)
Volition, etc.
Would I(I would) Would we(We would)
Would You(You would) Would You(We would)
Should he(He should) Should they(They should)

In subordinate clauses should is used in all persons to express futurity, would to express volition, etc.

In indirect discourse the usage is similar to that in direct statement.

The teacher said that John would win the medal.

Exceptions. Should is often used to express moral obligation.

You should be honest under all conditions.

Would is sometimes used to express frequentive action.