If you cannot fit another HDD into the machine (even just resting it on the base of the machine if there are no spare drive bays) then the simplest way is as staed above by setting up a simple peer to peer network.
However you will need two ethernet cards (£10 each approx) plus a cross over cable (£4 approx) plus the time to configure networking on both PC's.
If an IT dealer will do it for £30 I'd save myself the hassle and let them do it !!