I have modern, double glazed windows. They open outwards, by twisting the handle - in the middle, at the bottom of the frame - 90 degrees, from horizontal to vertical position and this unlocks the four hidden (when closed) catches that are found at the bottom of the frame. It is then pushed outwards, and the top end slides down a bit.
When working properly, turning the handle takes a bit of effort, but now it moves easily.
I have removed the handle by undoing the two screws that hold it in place. Inside, it looks a bit like the inside of a door handle, with a square slot, and the handle has a square shank which it fits into. Turning the handle turns the "round bit" which has the square slot.
The square shank is not worn out, and still turns the "round bit".
If the handle turns but the window mechanism doesn't move it could be that the linkage inside the window has broken or become dislodged. You will need to get this repaired by a double glazing company. Try looking in Yellow Pages or Thompson Local and get at least 3 quotes for repair.
Had this happen to tthe front door some time ago and it took the man about half an hour to fix, cost �60 labour and �20 for a new mechanism.