I keep meaning to do a step by step guide on this too, so if I may, I will answer beyond your actual question.

But yes, you can do it online, the problem is that it is sometimes difficult to avoid making a telephone call at some point. If you changed your ticket after initial process, or didn't do it via BA.com, then a telephone call is probably inevitable.

Apart from that, this process seems to work best:
- Don't check-in for the your original flight. If you already have a good seat on that service, and you may potentially need to travel on the original service, then you best leave it in MMB without checking in. If you do check-in and change your mind, then you'll have to get yourself offloaded, see post below.

- At midnight local time for departure, use BA.com to go online, change your flight for free via the link in MMB:"Change date/time of my flight" . You will need to have the number of your credit/debit card handy for ID purposes, the original e-ticket email will give you a hint as to which card was involved in Payment Information section.

- Wait until you get an automated email with the changed e-ticket receipt, this takes at least 10 minutes, but until that happens you can't do anything more. I tend to leave it until waking up.

- You can then select seats, though Theoretical Seating should have actually found the best option anyway (and that seems to work well).

- Check-in online: On BA.com that's fairly easy, follow the usual route, perhaps email yourself a copy of the boarding pass. On the App the problem is that your old flight will linger awkwardly, but if you leave the phone connected it may refresh itself by the time you wake up. And/or log out, log in. In the App go to My Bookings, refresh if necessary, find the flight under its new time, then go into "View and manager more flight details", and then Manage My Booking in blue at the bottom, and check-in there (this uses BA.com, rather than the App's logic). If you try to check in via the usual App route, it may well say that there is no ticket number attached - actually there is, it's just the App may not pick it up.

- Still on the App, having checked in, go back to "View and manage more flight details", refresh, and the bar should change to View Boarding Pass, and then you're fine to go.

- If you don't get the App to work for yourself, but you did get the email boarding pass, then you can quickly reprint the boarding pass at the Self Service machines if necessary.

If none of this works, then at the airport they can sort it all out, but if you haven't checked in you must be at the airport an hour before departure, since check-in closes at 45 minutes.