1. Select a Snapchat friend (swipe right and choose a friend in your Friends list or choose a group you created in Snapchat).
2. Click on Settings.
3. Select Do Not Disturb (If you do not see the do not disturb option, update to the latest version of the Snapchat app).
This will disable all notifications from that Snapchat user or group.
If you want to disable do not disturb on a friend and essentially re-enable notifications, repeat steps 1-2 and then choose Turn on Notifications.