I recommend checking out the crazymeds.us wiki and forums on questions like these. The wiki has what's basically a plain English translation of the prescribing info, and since it's a meds centered site, there are a lot of people who have taken it and forums specific to different drugs.
Your doctor should be doing regular blood tests right now, and they should continue less frequently as time goes on. Lithium therapy is determined by blood levels, not absolute dose, and the range is .6-1.2. It can take a few weeks to work after you get to that level. You need to drink plenty of water while you're on it, and watch out for med interactions. Read the sheet that came with it, find the patient information online, or go to your local pharmacy and ask to speak to the pharmacist about it, and ask a pharmacist about any new medications, including over the counter ones.
Weight gain, tremor, and acne are apparently the most common side effects, but many people have fewer side effects after being on any medication for a while, and you never know which side effects you will get until you've taken it. If you haven't noticed any side effects so far, there's a better chance that you won't get bad ones later, since side effects (maybe except for weight gain, which you should keep an eye on) are usually the worst on start-up. Your doctor should do regular blood tests for things like thyroid function as well.
Drink plenty of water because Lithium also can make you dehydrated and dry mouth .
In most cases, lithium has to get to a therapeutic level before you start to see results. Blood draws are taken to see what your lithium level is. I take a low dose that does the trick but it's low enough that I don't have to get my levels drawn. I know it takes some adjustment.
I had problems with tremors when I first started taking it. It doesn't seem so bad now but maybe I've just gotten used to it.