Read carefully jwolf's post, it's full of good advices. Kris has some things that need to be precised, but mostly good too.
For trade, start thinking about it when you get to trade 3. Send a few merchants in some CoTs, and look how long they stay in it, how much they made you earn, and if it's worth the cost of having them there (
including the costs of failed attempts). If you're negative, abort, and either try elsewhere or later.
Interestingly, some rather poor CoTs are in fact very interesting to start trading in, because they don't get much of a competition, which means your merchants stay put much longer.
Dont necessarily spend your january's leftover on merchants. If they don't return a positive benefit, you'll be investing less in technology. And it's technology that will give you the edge, if you maintain a pure infra/trade research until levels 4/4 or 5/5.
For your wars, avoid all battles. Early on, the game engine is unreliable, too random, and you'd suffer huge losses for little gains. And the AI'll always have much more troops than you. Troops are expensive to raise, so avoid cases where you have to recruit them. So, avoid battles, focus on multiple sieges. Don't research land or naval techs, since you're gonna avoid battles. Focusin' on economy is better, as later you'll have a much better income. Usually, the AI is first at land 9 while you're still at land 2 or 3, but at the same time you hit infra/trade 4/4 or 5/5, and before the AI gets to land 14 you'll have bested it there. From then on, it's cakewalk.
A final note : manufactories are good. Expensive, but real good. Imagine that for a cost of less than a thousand ducats for the first couple of them, you get a boost of 66-72d to your annual income, without even counting their other "side" benefits : 5d/month in tech-investments, and 6 or 12d annually to your monthly income (
0.5 or 1d/month). Nothing beats early manufactory's benefits, they pay for themselves in barely a dozen years.