You can access the new feature when you long press on a friend's name or tap on the hamburger menu in a chat thread. There you'll find new buttons to either send your location or request for your friend's -- the map with that info will then appear in your private convo. You don't have to worry about random people asking for your location either: the feature will only appear for mutual friends, and you can always switch off requests if you'd rather not get any at all.
If you do share your location with anyone, it'll only work for eight hours after you last opened the app. You can also cancel their access anytime you want. Snapchat has confirmed to TechCrunch that the feature has been rolling out to both iOS and Android users over the past few weeks.
Update 5/225/18 1:19PM ET: This post has been updated to clarify details about the "Send and Request" feature, including that you could always choose to share your location with select friends in the app. Location tools in Snapchat are and have been opt-in.