The next add/drop period is August 20-22, 2019.
As long as you obtained your adviser's permission to register for fall classes back in the April registration period (or since then), you don't need any new permission to add/drop now.
Not sure if your adviser gave you permission to register? Check by logging into Student Planning via myBarnard.
If you don't have permission to register, you'll see this notification in the upper-righthand corner:
If you do have permission to register, no notification!
If you think you should have permission but don't, be in touch with an adviser or dean ASAP before your next registration time.
Find your individual registration times on myBarnard
Register as usual by logging into Student Planning via myBarnard.
There will be additional add/drop periods in August and September (you'll see these if you look up your registration times on myBarnard)
The final add/drop/"shopping" period will be Sept 3-13, 2019
Final Registration Deadline is Friday, September 13, 2019.
Keep track of these and other deadlines via the Senior Class Deadlines gBear calendar.