Both of these words have many different uses and meanings, but these are the ones which tend to confuse Spanish speakers the most:
'Like' means 'similar to', for example 'He swims like a fish' or 'She sings like an angel'.
'As' refers to a role, for example 'He went to Cuba as a tourist' or 'She works as a nurse'.
'As' is also used in comparative sentences, for example 'He's not as clever as his brother'.