Je me lève normalement à 7h00 - I normally get up at 7am.
Normalement, on devrait partir dans 10 minutes - We are supposed to leave in 10 minutes (if all goes well).
Related: normal - normal, natural
Normalement is a semi-false cognate. While it can mean "normally," it is often used in a more figurative sense, as in "usually" or "it's expected." For example, it was 12:15 and I was waiting to join a tour group in a wine cave. The proprietor said, "Normalement, ils doivent arriver à midi." In English, using "normally" here would make it sound like this group visits the cave regularly at noon, whereas what she meant was "They were supposed to be here at noon."
(click the little graphic below to hear the Mot du jour pronounced)