You'll find stories from friends and popular accounts in a navigation bar at the top of your Instagram feed. Once you tap into one, you can move back and forth through the slideshow at your own pace. You won't be able to leave public comments or like anything you see in a story, but you can still send a private message to the author. The latter change is a sign that this endeavor doesn't quite fit into Instagram's existing feature set.
Naturally, stories will follow whatever privacy settings you've chosen for Instagram. You'll also be able to hide them from specific followers. I haven't had a chance to test out the feature yet, but judging from the screenshots and videos, it also looks like there are plenty of editing options for making your stories "fun."
While a bit shameless, it makes sense for Instagram to adopt one of Snapchat's defining features. Since its inception, Instagram has been focused on curated feeds. Those still have a place today, but the company also needs a more relaxed form of posting to compete with Snapchat's breezier style, where you don't have to worry about framing the perfect shot for posterity. Instagram will be rolling out the stories feature on iOS and Android over the next few weeks.