begin, commence, start

Begin is the more general term:

• Until I can start my car, I cannot begin to finish my chores.
• The meeting will begin at 8:30 exactly.
• My course in Canadian history begins (or starts) on Tuesday, May 15.
• Some people say the world began with a big bang.
• Do not begin writing until the bell rings.

Commence is more formal than begin or start:

• The ceremony will commence promptly at 11 a.m.

Start usually applies to physical motion:

• Ladies and gentlemen, start your engines!