1) Remove clutch and inspect the bearing. If it's shot you can't go any further. Shaft/flange wobble means a new clutch because the bearing is not easily serviceable. Fwiw a bad clutch bearing can quickly kill a water pump and vice versa. It's why they're usually replaced together.
2) Remove screws holding clutch halves together. They can be tight. Separate the halves being careful not to damage the O ring. There aren't any springs or small parts that'll come flying out so don't worry about it.
3) Drain what remains of the old fluid and clean. There aren't many solvents that cut silicone oil well but do what you can.
4) Inspect the control valve. It's a metal strip that uncovers two ports as the thermostatic coil twists the shaft it's on. A simply device really. If you want to test it place the half with the coil down in a pan of water with the water just covering the coil but keep the coil off the bottom of the pan. Heat the water while measuring it's temp. The ports should begin to uncover around 160 F and be fully uncovered by 200 F. A little "sticktion" in the mechanism is normal. If the thing needs calibration the holes are elongated. You'll see what I mean when you're in there. You can also heat the coil with a hair dryer just to see if it's working.
5) You'll need 3000 centistoke silicone oil. Get it on ebay or a hobby shop, it's used for RC cars. I like the Mugen brand but any 3000 cst silicone will do. It comes in 50 ml bottles (which is exactly the amount needed) for around 6 bux. Btw don't buy an oil that's sold by "weight", only buy one sold by centistokes. All Japanese RC oil is sold by centistokes, Mugen included. If they don't have 3000 cst buy what thay have and use a viscosity calculator to mix 3000 up. GE Silicones has a nice one on their site but damned if I can find it at the moment. You plug in the centistokes of what you have and what you want and it coughs up the percentages to mix. I'll keep looking for it and edit later.
6) Pour the 50 ml of 3000 cst into the half where reservoir is. Iirc that'll be down behind the coil but it really doesn't matter where it goes as long as you get it all in. Clean then swipe the O ring with a bit of oil and put the thing back together. Torque the screws good. I recommend threadlocker. Inspect and clean fan. Install fan to clutch and install the assembly back onto engine. Be happy.
A few other comments: The clutch is designed to run the fan at about 40% clutch speed at idle to provide cooling at slow speed. It'll drop off as rpm increases and only speed up again as the coil heats up. When in doubt the clutch can be tested on the car as I mentioned earlier.
For the curious some info and specs from Hayden about clutches:
http://tinyurl.com/2cceed
Edit: Forgot to mention. The old oil had to get out somewhere right? It's usually through the shaft seal. Some people add a capful of seal sweller to the oil during a refill. Lacquer thinner works. I've used power steering or transmission seal sweller but any similar product will do. Than again I've done clutches without adding anything and they lasted for years so don't fret over it.