"The teacher is very boring."
Translation:Læreren er svært kjedelig.
To me "svært" is a bit more formal, but they're otherwise interchangeable in meaning. Some may see "svært" as a bit stronger than "veldig". I can't really think of a situation where either of them would feel out of place, so you're pretty safe regardless of which you choose.
Beware that "svært" is also the neuter form of the adjective "svær", which means "big" or "huge".