log into ba.com
'go shopping' (ie click on earn miles, then shopping partners)
use the click-through onto play.com
shop normally

because you've surfed to play.com through ba.com Play will tell BA how much money you spent with them that day and will credit you with BA Miles at varying rates (2 BA miles per £1 for play iirc)

be careful if you are using this method to keep your miles account active as it does take weeks for the miles to credit, and sometimes transactions are missed.