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.
If it's any consolation, according to the historical records statistics, we are WAY overdue for a bright supernova to be visible in the northern hemisphere. They should occur about ever 100 years on average, but the last one visible occurred in 1680, the remnants of which are now called Cassiopeia A. The 1987 supernova was actually not in our galaxy at all, but rather in the Large Magellanic Cloud, a dwarf, irregular companion galaxy to the Milky Way. It was visible only in the southern hemisphere and I believe it achieved a visual magnitude of only 3, which is medium-bright. There may have been supernovas in the Milky way since 1680, but if they did occur they were hidden behind dust or star clouds, and therefore not visible to us. But astronomers are very anxious to view a relatively nearby one, and as I've said, we're long overdue for one.