The first thing to understand while differentiating between ‘should’ and ‘would’ is that both of them are modal auxiliaries and both are usually used in requests, questions and offers. Usually, would and should are used as the past form or less definite form of ‘will’ and ‘shall’.

  

 Should - Should is used either to suggest something or to talk about obligation. Should is used with first person pronouns in conditional sentences. For example:

 He should leave now

 They children should visit the museum.

 I think I should go pay her a visit.

  

  

 Would - Would is generally used to talk about something we used to do in the past or some past habits. Would is used with first, second and third person pronouns in conditional statements and questions. For example:

 When they were young, they would often spend time listening to psychedelic rock music.

 The man would keep grieving the loss of his dead wife.

 If you would come by evening, we could go for a night show of the latest Iron Man sequel.