King Rama V had the place built to welcome a group of Portuguese envoys, and he himself only stayed there once.
The palace was converted to a monastery during the reign of Rama VII (1925 to 1935).
About 30 monks are cloistered there today living a particularly strict Buddhist existence -- they aren't even allowed to handle money. It's quite a centre of activity among Thais who come to make Buddhist merit or consult the monks.
If you're very keen you can inquire about staying at a retreat in the temple complex, but this is not for tourists. There's really nothing special here, including the view of the city, and unless you're a Buddhist or student of the faith there's no real reason to make the trip.
Green songthaews leave from in front of the police station and will take you there for 10 baht. From the road, it's a brisk 10-minute walk up the hill to the wat at the top, which sits behind Khao Wang School. Watch out for the dogs as there are some quite nasty ones along the way -- though no monkeys, thankfully.
The Travelfish newsletter is sent out every Monday and is jammed full of free advice for travel in Southeast Asia. You can see past issues here.