Note: The following summation is a loose guide and is flexible depending on your desired victory.
Production, Production, Production. I'd recommend playing as England (navy and spies), France (culture), or the Celts (faith) for your first go. Pick a standard-sized map; continents is best and found your capital city.
Build a monument for culture, go down the Liberty policy-track, and pump out 2-3 more warriors. Explore and gain experience from killing barbarians - keep one unit in your city to avoid any pillaging. Tech-wise, if you're not playing Boudicca, try for Animal Husbandry or Pottery first, and get the techs that will allow you to improve your tiles. Early gold, food, and production helps to no end.
Build a couple of military units and continue founding cities. By turn 75 or so, you should have at least three. Make sure you research writing fairly quickly (no need to rush though) and build libraries in your cities. Go for the early two military techs and then beeline for Philosophy - create the National College in your capital while still building military units or markets in your other cities. Watch your income and maintenance. You should have two -three workers by the time you complete the NC, and by then a military of about 8-9 assorted spearmen, archers, and (maybe) horsemen. Research mathematics for the catapult and station one in your capital.
Continue building yourself up - markets, lighthouses, WONDERS, etc. - but don't build unnecessary buildings (maintenance costs are high). When you've researched Iron Working and the tech required for Trebuchets, ATTACK your closest neighbor if your third or fourth cities border his lands; cripple him, and, if possible, take his capital. Now with him crippled, you will be relatively free to build up in a somewhat safe environment. Continue researching, building culture and science-related wonders, and make your way in the world.
If you see other civs who are close to victory, bribe their neighbors to war with them if you'd rather not attack yourself. Keep a siege weapon in your capital and stack a small but technologically-advanced navy off your coasts. You should be safe from invasion and in a comfortable position. As you near the industrial and modern eras, focus less on growth and more on production (workshops, factories, etc.) - buy coal from your neighbors if you absolutely have to. Round up a few CS allies (cultured, maritime, or mercantile) and build as many useful wonders as you can.
As you near a Scientific Victory, make sure you have a strong military and a respected diplomatic position. Stir up conflicts if you have to. Make sure you don't neglect happiness and culture growth.
Sorry for the short, choppy guide - but it should be enough to help you win!
Good luck!