Quite possible, and it has happened before and is often recorded for posterity. Tycho Brahe saw one once, and he's a 'founding father' of modern observational astronomy.
Basically it'll be a very bright star where there wasn't one before. It'll move just like all the other stars, it won't flicker or drift etc. It'll stick around for days or so, and slowly dim over time. It's possible to be bright enough to see in daylight.
But they are incredibly rare to have one bright enough to be visible to the naked eye at all. I think only a few have happened in recorded history.
Rule of thumb: If you think you saw one, and it isn't in the papers the next day (maybe 2) you didn't see one. It'll be BIG news in astronomy circles.