What you describe is probably a Donut or Doughnut Washer - a thick, soft, rubber washer compressed hard by a metal pressure plate with a wing nut and bolt each side at the back.
This is a normal arrangement on a close coupled cistern - leaks here can often be cured by just tightening the wing nuts.
You may wish to squint along the join line from the side - the thick rubber washer should be relatively thin and above all parallel - sometimes the down pipe from the cistern is too long - interferes with the material of the pan and tips the cistern slightly forward - in this case you will not get a satisfactory seal unless you saw an eigth of an inch or so from the end of the pipe.
If you need to change it a Dounut washer kit may bought quite cheaply from a DIY store...
http://www.toiletspares.co.uk/images/st/st_CC_kit_doughnut_washer_new.gif
To gain access turn off the water supply to the cistern and flush it. Undo the water supply union. Remove the wing nuts from the donut washer bolts. Remove two screws holding the cistern against the wall. Gently lift the cistern vertically and tip any excess water into the pan.
Some people suggest sealant around the washer - I don't agree - it's a low pressure seal and the pressure plate should be good enough to stop water coming out if it's properly squared up and tightly compressed.
On reassembly do not overtighten the screws into the back of the cistern else it may crack - snug is good enough.
First time you do it expect to take 30 mins or so.
Good luck...
Peccavi
June 2010