Discount railcards are available for people aged 60 and over, for people aged 16 to 25 (or mature full-time students), for two over-16s travelling together, and for those with a disability.
You'll find they pay for themselves pretty quickly if you plan to take a couple of long-distance journeys or a handful of short-distance ones. Fill in an application at any major station. You'll need proof of age (birth certificate, passport or driving licence) for the Young Persons and Senior Railcards (proof of enrolment for mature-age students) and proof of entitlement for the Disabled Persons Railcard. You'll need a passport photo for all of them. You can also buy railcards online, but you'll need a UK address to have them sent to.