Example 1
Lindsay's ecologically minded friends are really into dumpster diving for dinner; however, Lindsay would rather sit down to an elegant nine-course meal.
We're with Lindsay on this one. Supping on someone's day-old salami sandwich seems a bit hard to, uh, swallow. In this example, the conjunctive adverb however is used to link the independent clause about dumpster diving in the first half of the sentence to the independent clause about swanky restaurant dining in the second half of the sentence.
Example 2
The spy's cover was blown. Therefore, he returned to headquarters to await a new mission.
This never would've happened to James Bond. Or James Bond, Jr. In this top-secret example, the conjunctive adverb therefore links the two sentences because their ideas are similar. The second sentence, about the spy having to go back to HQ, is the direct result of his cover being blown.
Example 3
Judy is allergic to gluten; otherwise, she would have dived into the basket full of scrumptious garlic bread headfirst.
It's okay to feel sorry for Judy. Garlic bread is delicious. It's not okay to miss that, in this sentence, otherwise is a conjunctive adverb because it links two independent clauses that are closely related in idea.