Fixing depends on model. I had the same problem with a RCS4450c chainsaw. It took a little working out but you do not have to dismantle the whole saw. The whole job takes less than an hour
For many petrol models:
Remove the clutch/chain drive cover by removing the two nuts. Remove the chain and bar by sliding the bar towards the clutch to provide slack.
Remove the starter cord pull (4 torx screws on my model).
Lock or brace the nut on the centre of the starter clutch with an appropriate spanner or socket.
Undo the drive clutch; it is the centre of the clutch assembly with an arrow and 'UNDO' stamped on it. I managed this by grasping it firmly with vice grips but see other answer for other methods to undo it.
Once undone, remove it and the small roller bearing race.
You should now have access to a nylon worm drive which turns the oil pump. On my saw the nylon drive had stripped. It appears to be sacrificial as the oil pump drive itself is steel. If this nylon part is at all damaged, replace with new. These are available from http://www.ryobispares.co.uk/html/chainsaws.html
Part number 518458001 but do check against your model. be prepared to pay somewhat more than the price quoted on the spares list. The part is listed as about £3. I had to pay £21 for two including postage.
Rebuild in reverse order. The worm drive needs to be gently screwed in to engage with the oil pump. If you push it you will undo all your good work by knackering the thread.
Replace the roller bearings. Engage the tangs on the outer part of the clutch with the cut-outs on the worm drive.
Replace the washer then screw the centre of the drive clutch back on - left hand thread so anti-clockwise. It does not need to be massively tight as the rotation of the clutch acts to tighten it.
Replace the starter pull cord mechanism. Ensure any wires are correctly routed.
At this point it is worth starting the saw to ensure that the oil feed is indeed working. Within a few seconds of start-up, oil should feed out of the oiler hole. If not then you have a different problem (has it got oil in it?)
Replace bar and chain. Replace clutch cover and adjust chain tension. Again start the saw and ensure that a small amount of oil is being flung off the chain at the end of the bar.
Job done.
Nanook of the north
January 2011