I must clarify this a bit. St. Andrews is not a club, it is a golf course. It is in fact a public golf course owned and managed by the St. Andrews Trust. Anyone can play there. It is also public land, while playing you will find people walking on the property.
The actual club is the R&A, The Royal and Ancient Golf Club. It is this organization that owns the building that we all see behind the first tee at the Old Course, St. Andrews. It is this body that is thinking about a vote to admit ladies to thier membership.
The other thing mentioned was that Royal Troon is also thinking about this move. This is not true. Royal Troon has always had a Ladies Section, Troon Ladies. It was founded in the early 1800's, 1816 I think. They have thier own clubhouse (men not invited in!) and thier own golf course, the Portland Course at Royal Troon. Men are allowed on the Portland Course when the ladies do not have times booked. Ladies can, but usually do not play the Championship Course at Royal Troon.