Should’ is the past tense of the word ‘shall.’ When using the words ‘should have’ you are talking about something in the past that you ‘ought to’ or ‘might have’ done.
Here are some examples:
“I should have gone with you.”
“I should have studied more for my test.”
“I should have read the directions before starting.”
“I should have eaten breakfast this morning.”
“I should have listened to your advice.”
“I should have married her when I had the chance.“
‘Shall’ is something that will take place or exist in the future.
Here are some examples:
“I shall leave tomorrow.”
“I shall finish the job next week.”
“I shall see it tomorrow.”
“I shall go outside if it’s nice out.”
“I shall pay for this later.“