These are only suggestions. Experiment a bit, and of course the different civs have their own strengths you can play to...
1. Start on an easy level. There's nothing wrong with playing on the first level if you've never played before. Even if you've played Civ 1 or Civ 2, give yourself a chance to learn the system first before getting ambitious
2. You will need a unit to defend your city against the risk of barbarians, usually. That means build a warrior. You'll need a few more to go exploring, to reveal the map. You need to find out where to send settlers, etc.
3. Build settlers. The AI civs expand like crazy, and you need to grab some good room. try to make sure you time it so the settler is ready just as you get a third citizen - any earlier and the settler will wait for the next population, which is wasted production. Later and you aren't expanding as fast as you could be. Try to build cities in 'good' locations, near bonus resources or luxuries if you can - the extra bonuses are valuable at the start. But don't wander the map looking for them - a settler doesnt produce, so you want the city pretty quickly.
4. There are two schools of thought on city location:
(a) Build them as close together as you can - every other square, chequerboard style. It gets a lot of production going quickly, and minimises corruption due to distance;
(b) build optimal locations - spread out to cover lots of land, in the best possible spots 9rivers, bonuses, etc). This is more efficient in the later game but can slow you down at the start.
Its a question of personal taste, really. And also how close the other civs are; you may have no choice but to pack them in.
edit - more added to answer other questions
You also want to try to locate your cities around your capital, not all in one direction if you can. that's because capital-city distance can affect corruption in the city too, so you want a central capital if possible.
5. Techs - really depends on your civ to some extent. Some civs have pretty potent UUs - unique units. You want to get them as soon as you can. So the Egyptians will want to make sure they can built War Chariots, and so should research the wheel asap, if they dont start with it. Similarly the romans want Iron Working (for legionaries) etc.
- also, some techs are needed to reveal certain resources - you want to know where the iron and horses are to get a chance to cliam them by building a city on or next to them. So techs that reveal resources are good.
Some people recommend making a beeline for the Great Library (Literature) so that you can build that wonder, and get all the other techs for free as the other civs discover them. Its not mandatory though; at the easier settings you can get a technology lead without if you play that way.
A big decision to make is style of play. What you build will vary massively between a kill, kill,kill strategy and a nice-to-my-neighbours strategy. Obviously if you are going to try to wipe out the others you need lots of military units, so you need the tech for the good ancient units - Horse riding and/or iron working, basically. If you are going for a cultural type win then the earlier you start building temples etc, the earlier you start to get a cultural lead.
