I don’t know about this “Wonders of the World” scenario (did that ship with the game?), but there are a few things to learn. First, expand early and often. As soon as your capital city is big enough, build a settler. As soon as the new city is big enough, it builds a settler, too, as well as the capitol. Continue this way until you run out of land area to expand to, and start again as soon as you have access to ships.
Second, decide right from the beginning what sort of victory you’re going for, or at least whether you’re going for military or peaceful victory. Either way, pick your civ for what you want. The Greeks, for instance, are great for science, and the Germans or Aztecs are a good choice for warfare.
If you’re going for a peaceful victory, try to stay out of wars. Easier said than done, I know, but one key is to trade with everyone you can. Ideally, you want to be trading them something they need (the perfect trade is to give a luxury or resource for a tech), but even if it’s going the other way, they’ll be reluctant to declare war on you, lest their reputation suffer. If you break a trade or treaty agreement by going to war, then nobody else on the planet will ever agree to that trade or treaty with you again.
Even if you don’t plan to fight wars, they will happen some times. The best defense is a good offense. Even if you’re not looking to gain territory, you need some offensive units to chase their guys out of your territory. Until you get to Steam Power and build railroads, it’s essential that these counterattackers be fast, so don’t even bother with swordsmen (unless they’re your unique unit).
Except on the very easy difficulties, you won’t be able to monopolize the Wonders. Decide at the start of the game which ones you can’t do without, which ones would be nice to have, and which ones you don’t care about (here’s a hint: The Oracle and the Great Wall are completely useless). For the must-haves, you’ll want to prebuff: Figure out how long it’ll take to build the Wonder in the city you want it in, and how many turns it’ll take you to get to the appropriate technology. Then, in that city, start building a Palace (or another Wonder, or a very expensive city improvement) before you get the technology that allows that Wonder. When you get the tech, switch production from the Palace to the Wonder, and if you’ve planned it right, it’ll be one turn from done. For your optional wonders, be prepared to switch from one of them to another, when (as is likely) someone beats you to one of them.
And, of course, as with any game, practice, practice, practice. There are a myriad of little tricks which help, but it would be hard to list them. You’ll discover most of them on your own, one by one.