The cable from the ceiling will enter the body of the flourescent light trough a small hole and the three wires will be secured in a terminal strip: Earth Live & Neutral.
You will need to arrange a similar connection system for the new fitting and your local DIY store will be able to advise a low cost solution which you can hide either in the body of the new light assembly or in the ceiling void.
I have thrown away my kitchen spots - continually replacing blown bulbs and a magnet for airborne grease and dust - and have replaced them with flourescent tubes - no failures for over a year now, money well spent & better light. Keep the old - just in case...
Good luck...Take care...
Peccavi
April 2009