Just follow your nose to the top of the slate tips.
The main footpath up the Old Man via Low Water goes right though the lower workings where there are lots of buildings to investigate.
Higher up the mountain and away from the footpath in the red circle is where you want to look.
There are three interconnecting ways in that bring you out at various heights in the chamber.
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If you want maps and exact locations, theres an inexpensive leaflet on the CATMHS shop page.
http://www.catmhs.org.uk/pubs.php The Coniston Old Man Trail . £1.00 plus 80p p&p