If you are making a suggestion, there is no difference in meaning between 'Shall we take a walk?' and 'Should we take a walk?' Both have the same function. A speaker of American English would probably say 'Should we take a walk?', as 'shall' is rarely used in everyday modern American English. A speaker of Commonwealth English would be more likely to say either 'Shall we go for a walk?' or 'Should we go for a walk?'. 'Shall' and 'should' are interchangeable in these cases. The modal form 'should' is also used to refer to a course of action which is prudent, advisable or expected. What you 'should' do is what is wise, recommended or what you are supposed/expected to do. For example 'I hear that Jane has just had an operation. Do you think we should send some flowers?' 'Should' in this sense is similar to 'ought to'. In sentences like these, 'shall' and 'should' are not interchangeable. I hope that helps.

Should is the past tense of shall, as explained here: http://www.myenglishteacher.eu/blog/english-grammar-shall-vs-should-with-examples/ Lee is also right. Technically should is the past tense of shall, but in practice it's mostly used as he says. When Americans are sincerely asking for an opinion, they usually use "should." "Shall we go for a walk?" -- Speaker usually is asking someone to come with him or expects a yes "Should we go for a walk?" -- Speaker is questioning if they actually should or should not go. Maybe it looks like rain and he wants your opinion.

In American English, as Su.Ki said, we don't use "shall" much. Usually when we use it, we are trying to be "cute" or to act "gallant". It is normally used as a polite request that you expect a 'yes' answer to. Here are some examples. - Are you ready? Let's go then, shall we? - I'm tired. Let's rest a moment, shall we? - Shall we dance? (There is also a song by this title from the movie "The King and I".)

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