''Should'' is mostly used for advice or suggestion. ('We should meet again on Friday'). ''Shall'' is a formal version of ''will'' ('I shall/will call you soon') The problem with modal verbs is they can also have a different meaning sometimes. ''They SHOULD arrive in the next hour'' (deduction) ''Call us if you SHOULD have any problems'' (conditional) These are less common, but still cause problems.

"Shall" has same or similar meaning as "Will". In British English, most of the people would say "I shall go to school.", but in American English would say "I will go to school." Lesser people would use "Shall" now, because the past tense of "Shall" is "Shan't", "Shan't" is old style english, we just use "won't" (the past tense of "will") now. The meaning of "Should" is used to say what would have been right or sensible, but was not done.

Should- "It would be best to do..." Shall- "I would be best and I will do..." Does that make sense? Should is more of a uncertain suggestion, while shall is very definite and assured.