Honestly, this is a five minute job.
I spent the weekend watching a fan that looked almost ready to fall from the ceiling. Rather than calling an electrician, I asked around at work, and got some quick tips for fixing it myself.
It took about five minutes to find the root cause of the problem, and sort it out. Thanks to the great guys at Electrician To The Rescue for the tips.
All you need is a screwdriver, some pliers, and a step ladder.
Step 1: Check the Drop Rod
This is the main step in the repair. The rest is turning screws.
Most ceiling fans hang from a drop rod. The ball joint should be properly engaged to your support bracket. This is held in place with a cotter pin that runs through the rod and into the mount. If the pin is damaged, or bent, you're going to get a wobble.
With pliers and a new pin, you can fix this one pretty easily - all mechanics, no electrical work involved.
Step 2: Repair Uneven Blades
If your fan has had an impact, pretty much ever - whether it's with a hand raised a bit too far, a stray tennis ball, or a startled (and probably somewhat confused) small mammal - you're going to see some damage.
This was, it turns out, the problem with my own fan. I have a vague memory of hitting my head with the blades, and it seemed my skull did a bit of damage to the equilibrium.
The blades should hang equidistant from the ceiling. If they're not, if they're warped or bent, you need to replace them. These can be bought online for a pretty good price. Hey, if you're lucky, the manufacturer might even replace them for free! If you're me, you end up paying ~$50-$100 AUD.
It's pretty easy. Turn off the power to the fan, unscrew each blade in turn. Replace with the new blades. The thin end goes in the bracket; and then, screw in place (or, bolt, depending on the mount).
Turn the power back on once you're satisfied everything's secure, and test.
I had no more wobble after this - but I did have to tighten the screws a second time. Mostly because I'm paranoid.
If you're struggling with this, it's not worth messing around - call an electrician.
Step 3: Tighten Everything
If there's a screw, nut, or bolt, make sure it's tight.
The support bracket should be secured to the fitting very tightly. If it's not, you're in for a wobbly time.