Seat61 has great advice, so do look at that.
You can also look at the UK National Rail journey planner: https://ojp.nationalrail.co.uk/service/planjourney/search
You select your route, date, and trains, and then it directs you with a click to the relevant train operator's website to buy the tickets (in this case, it's Great Western Rail)
There are 3 types of tickets that are relevant for you:
Advance - Buy in advance, sold in limited numbers, subject to availability; ONLY valid on the date/train specified.
Off-Peak - Buy any time, travel off-peak.
Anytime - Buy any time, travel any time.
I traveled in June, London to Moreton-in-Marsh roundtrip ("return ticket"). I bought them before leaving the US. I started at the National Rail website and made the purchase at GWR's webpage. I bought an "Off Peak Return" for GBP50. I didn't choose the Advance ticket because I wanted flexibility in train times returning to London that evening. I'm glad I chose a flexible ticket, because, as it turned out, I stopped off in Oxford on the way back, just to get a taste of the city for a couple of hours. If I'd been on the Advance ticket I couldn't have "broken my journey" (as they call it) without incurring extra costs--I'd have been tied to the specific return train I'd purchased. But with the Off Peak Return, I could choose any off-peak train back to London and best as I could tell, all the trains arriving in London after the morning rush hour were off peak so any evening train was fine.
If you buy your tickets online ahead of time, you just print them out from one of the kiosks when you get to the station. You'll need your confirmation number and the same credit card you used. But do make sure that you collect all the various ticket and receipt cards that the machine spits out.
On my train from Paddington to Moreton-in-Marsh, at some point on board there was an announcement that only the first 3 cars were going past Oxford, so at Oxford I just double-checked with a platform agent. Interestingly, there were no platform agents that I could find at Paddington. I was trying to make sure I was getting in the correct car but the only person I saw with a GWR uniform on turned out to be station cleaning crew. The ticket barrier was automated too, so no human contact there. It all turned out fine though.
(you're not taking the Secret Cottage day tour by any chance, are you? if so, you'll enjoy it!)