Step 1: Find a point along your journey that is a popular stop. As an example, along the London-Glasgow route, Preston is a pretty good place to break the journey.
Step 2: Do a side-by-side search for trains from London-Preston and Preston-Glasgow. If you’re using TrainLine’s Best Fare Search, you’ll need to open two different browsers.
Step 3: Find trains for each of the four "legs" that match up. This is the trickiest part -- you don’t want to book a London-Preston train that gets in a few minutes after the Preston-Glasgow train leaves. No one in the ticket office will have any sympathy for you trying to game the system.
Of course, the Golden Unicorn find is splitting a ticket on the same train (and then you don’t even have to get off), but make sure you double and triple check that it is, in fact, the same train. Match the departure time with the train company for both legs, and when you board the train, make sure you find a seat that's unreserved for the whole journey (or make sure you change your seat wherever you’ve split the journey). Once that’s done, though, you can lean back and look upon all those suckers who paid full price with well-deserved smugness.