Travel to London for 16-year-old

Marmaduke123

From Reading just buy the one day travel card including tube travel on the day from a machine or the counter. The machines have the Railcard option on the booking screen, but make sure to carry the physical Railcard with you

Use the transport for London (TFL) website to plan the onward journey from Paddington, and back to Paddington at the end of the evening. There may be a bit of a wait for a train at Paddington on the way back, depending on when she gets to Paddington

Lucius45

Any chance you can drop her somewhere inside the M25 like Hayes, Ruislip etc? Doing that will save you much more than any railcard will (it would be no more than a fiver in and fiver out of central London)

t0rt0ise

To get the extra underground discount you need to ask staff to add the card to an oyster card.