Use the adverb verily when you need an old-fashioned way to say "certainly." For example, you might say, "I verily believe that's the ugliest sweater I've ever seen."
You can use the word verily to mean "truthfully," although people may not know what you're talking about, since it's mostly found in very old-fashioned writing, from the Bible to Shakespeare. In fact, Shakespeare is probably the writer most associated with the word verily: "Verily, I swear, 'tis better to be lowly born," he writes in "Henry VIII." The root is Middle English combination of very and ly, originally verraily.