Emigrate vs Immigrate
Quick answer: Direction decides it: you emigrate FROM a country (exit) and immigrate TO one (in). The same journey is both, depending which border you're describing.
Emigrate
Verb: to leave one's country to live elsewhere.
“They emigrated from Poland in 1990.”
Immigrate
Verb: to come into a new country to live.
“Her family immigrated to Canada.”
How to remember it
Emigrate = Exit. Immigrate = In.
Common mistake
'She immigrated from Italy' — leaving is emigrating; pair from with emigrate.