When is it appropriate to use "can" in a sentence? Is it always better to use "may?"
They have different meanings. Can should be used to express ability or capability (Can he move? = is he physically able to move?; May implies permissibility or possibility (May he move? = is he allowed to move?).
"May I go out?" = Is it permissible to go out
"We may want you to come to dinner" = There is a possibility that we want to join us.
"Can I go out?" = Will I be able to go out - or will something prevent me
"We can have you to dinner on Saturday" = There is nothing preventing us having you for a meal on Saturday.