Head out towards Barrhead on the A736, take the left turn past Tesco towards Neilston. Stay on this till you get in to Neilston and turn left onto High St (church on your right, pharmacy ahead of you). Follow this road round, over the railway and the hill for just under a mile and you should see the quarry on your left next to an electricity pylon.
You can fit a couple of cars on the left-hand verge just at the entrance gate. Alternatively a few metres down the road there is a small road on the right you can park along the side of. The area on the left just before you get to the entrance is private Scottish Water land and should not really be used.