About a year ago I installed a new ceiling fan in my living room and when it was installed it was balanced nicely, but it has a little wobble.
How do I bring it back in to balance?
Most new fans comes with a balance kit. It includes a heavy clip and a set of stick-on weights. If you don't have the balance kit you can buy one at a big-box home improvement store.
Three things come to mind.
When installing ceiling fans I always use one of these braced boxes. They have some that are for new work, or where you have access to the attic. They also make ones for old work, where you can put the brace up through the hole and tighten it down until it bites into the rafters.
Cleaning and tightening will probably do the trick, if not some blades have a bit of adjustment in them. Failing that...
One time I left the fan on in my parent's cabin for six months after I had a party there. When we got back it was still going but vibrating like it had a missing blade.
My dad, bless his heart, just rolled his eyes and told me to deal with it: he'd only get mad at me if I couldn't fix it. I tightened everything I could but it didn't help. Finally I tried taping a rock to the top of each blade in turn.
I tried each blade: the third of four seemed to cut down on the vibration a bit. So I started taping pennies to to that blade. At around 10 pennies the vibration was minimal. Couldn't get it better than that, but it was good enough that my dad said "Ok, don't be such an idiot next time" instead of walloping me.
Besides cleaning and swapping fan blades, check to make sure it the down rod with the ball (if you have one) is properly seated in with the slot in the down rod ball with the tab in the bracket that goes to the fan box.
Your box is attached to a stud, right? Check to make sure your box did not come lose from the stud. This all will require you to take some or part of the fan down.
I balanced my ceiling fan with chalk and pipe insulation. Make sure the blades are screwed in tightly. I taped the chalk to the end of the pipe insulation, then slowly brought it up to the edge of the spinning blades. It leaves a mark on the heaviest place, so you put weight on the opposite side. I broke a lot of chalk, but it's cheap. You can use the opposite end of the pipe insulation to hold against the bottom of the blades to slow down the fan so you don't have to wait until it stops spinning on its own.