If the site does not have an incinerator of its own you will need to make one. Any rubbish that can not be burned on the campfire should be placed in the incinerator. The ashes should be removed at regular intervals and disposed of as above.
You will need a large metal can (an 'oil-drum' type is ideal). Pierce the can with holes all round and place over a fire. You may find it easier to fill the can with earth and use a large nail or spike when making the holes.