I disagree with the advice to get food online first; I almost always start with Bronze Working, then something food-related (if you don't have one for turning up), then beeline Alphabet. Chop to build Workers, Warriors and Settlers, then trade techs to get other early food and roads. If it turns out you have Copper in your start area, maybe even chop to get an army out and conquer a nearby capital. (Why found Buddhism when a neighbour can do it for you, eh?)
A popular early strategy/tech path is to beeline Priesthood, then from there Writing and Monarchy. With those two, the Oracle will give you Feudalism. Either learn Archery or to Alphabet to trade Monarchy for it, and you're packing very early Longbows - with this slingshot, Protective goes from being a generally weak ability to a fairy useful trump card.
If I have Elephants easily to hand, I look towards Horseback Riding and Construction. You've then got Elephants and Catapults; this combo can often trample the AI until Gunpowder appears. This path includes Mathematics, so Code of Laws is fairly close to hand to put Courthouses in captured cities.
If you have Priesthood and Pottery, the Oracle can get you Metal Casting. If a second city has a load of forests already reduced to a single turn cut (but not wholly cut!), you can immediately build a Forge and run an Engineer. He can rush you the Pyramids, or lightbulb Machinery. This works very well with Philosophical leaders. Sitting Bull has especially good synergy with this - Drill 3 Crossbows can make a mess of any foe lacking Horses.
Try to consider what works well with your traits and units; if you are Aggressive, then metals are even more useful. If you are Financial, getting Cottages online early is great. Carthage loves getting Sailing, Masonry, Compass and Currency on coastal maps - the Great Lighthouse becomes extremely powerful. If you've got Marble, the Temple of Artemis complements this brilliantly.