There's a thread at the top of this page with beginner tips, but if you've never played any of the Civ games, and have only had the game for a bit of time, most of the suggestions will probably go way over your head (or you'll have too many rattling around in there that you won't be able to get anthing out).
Here are some things I'd suggest:
1) Do the tutorial, it will give you some basics (about 10% of the game).
2) <optional, but eventually> read the manual. That will cover about 50% of the game. There is so much to this game that isn't printed in the manual - or even in the online help. If you have a hard copy, it makes good toilet material...
3) Play games. Some suggestions there:
- Play at the level just below Noble. This level is easier, but not so easy that you won't learn from mistakes.
- I think the first option (continents?) is a good one to start with. Usually you'll have one or two AI civilizations on the same continent as you, so it won't be like you're up against 5 or 6 AI at once, and you won't be all on your own (which is also bad because you won't learn early-intereaction).
- At first, don't worry about strategy... just go higgildy-piggeldy producing units & buildings and wonders. It will give you an idea of what things do.
- Later, start to specialize your city. Don't build things you don't need until you need it (or just before you need it). For example, an Aquiduct improves the healthiness of a city - if your city is already healthy, then don't build it.
4) Learn about combat. In those games, make sure you try out combat, and especailly pay attention to the effect of the three main types of units:
- Melee
- Ranged (archers and later gunpowder - although these are two very distinct types of units, I combined them to make it easier)
- Artillery (catapaults, canons, artillery)
- Armor (like tanks)
- Air (fighters, bombers, choppers)
- Navy (ok, that's six... but the first three will be your main army for most of the game)
Remember the power of combined arms (archers for defense, artillery for assaulting cities & doing collateral damage, and melee/tanks for invading the cities).
As for technologues/research, just go and try everything out at the beginning. Later on, after about 2-3 games, you can start to think about what you want to get to, and persue those techs earlier (or "be-line" to them).
Some tips:
- Build at least 1 worker per city, but even better, build 5 workers for your first 3 cities. Having them will mean a faster start even though your cities aren't growing while they're being created
- After the first 50 turns or so, make sure your border cities have AT LEAST 2 defenders in each city (probably 2 archers).
- When attacking, try to attack with artillery if you can make it, and have 2 units for every one defender if you're on the same technological footing.
- If you have nothing to build in a city, build military units. If you have too much military, either attack someone or change the city to produce wealth (which you can use to upgrade units or increase research). If you are already at 100% research/culture and STILL have money left over, then switch it to culture if it's a border city or research if it's not.... that will be REALLY rare though

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I think that's about it for my newbie tips. Really, the only way you can learn this game is by playing it, and it generally takes 2-3 games (after the tutorial) to get the hang of it. That's when you might want to look at the tips page (which covers things like chop-rushing, diplomacy, defense ideas, build orders, and so on).
And post here since this is an EXCELLENT place to get advice.