If you can be flexible about your travel time, there's a much better chance of making really great savings. Plus, you'll enjoy your journey more if the train is less crowded!
Generally speaking, try to avoid travelling between 0630 - 0930 and 1530 - 1830.
In terms of train ticket selection, you'll find that Off-Peak tickets are much cheaper than the fully flexible Anytime tickets. Whilst Off-Peak rail tickets are generally valid on trains leaving after around 0900, the times willl vary by route. The good news is that MyTrainTicket makes it easy for you to see which trains you can travel on when you buy an Off-Peak ticket.
Super Off-Peak tickets offer even better value, although they're not usually available till a little later in the day.
You will also find that, if you're searching outside peak travel times, you are more likely to see tickets for a cheap Advance train ticket available on your route - to help you achieve maximum possible savings.