You seem to be planning on using the ticket I mentioned above, which will cost £178.90 return for two, with a Two Together Railcard.
Valid on trains from London to Edinburgh from 0930 on a Wednesday, and any train back on a Saturday, within a month.
This is a Super Off Peak Return walk on fare.
You don't have to book it in advance, you can buy it from any mainline ticket office at any time, up to departure time.
They will also book seats for you, both ways, at the same time if you wish (recommended, free).
You can also use one route to Edinburgh and the other one back to London, and break your journey en route.
You can also change/refund the ticket if needed, for a fee.
If you want to book ahead, you can use any train operator's web site to buy the tickets.
They will either post them to you or give you a booking reference to pick them up at your departure station from an ATM.
To check times you can use Virgin Trains East Coast web site
https://www.virgintrainseastcoast.com/
Simply put in London and Edinburgh and the dates/times of travel, and your railcard details.
To select trains via the East Coast route, enter "Via York" in "Route Options". 1-2 trains an hour.
To select trains via the West Coast route, enter "Via Preston" (1 train an hour, usually involving a change at Preston to avoid the loop via Birmingham).
You should then see the £178.90 fare, and the trains it is valid on.
Click on the trains you want and complete the booking process to reserve a seat and pay.
You don't have to have your railcard to hand to buy tickets, but you do need to take it with you on the journey.
Note you don't have to stick to the trains you have booked if things change, except you can't leave London before 0930.
You just won't have a specific seat booked on other trains.
Web sites don't support booking one route out and another back, so if you want to do that you can book a seat on the other route separately, without buying a new travel ticket.
I hope this is useful for your trip, and that I have included the appropriate options for your dates.
A very similar fare/details apply to London-Glasgow.
Glasgow-Edinburgh off-peak return is about £15 with your railcard, buy on the day.
Trains every 15 minutes, takes 45 minutes.
PS I should also say that you start from London Euston for the West Coast route, and London King's Cross for the East Coast.
One stop between them on the tube, or a 10-minute walk along Euston Road (impressive in itself, past St Pancras station and the British Library).
All trains stop at Waverley station in Edinburgh.
Glasgow has two main stations: Central (from London) and Queen Street (main service to Edinburgh), another interesting 10 minute walk between the two.