Some essential tips:
1.Cultural victory is the easiest, because you don't have to conquer anything, and you can probably do it with just your capital. So, it might be good to start out on a small map and do a culture victory just to learn the mechanics of the game.
2.You will, however, be attacked, but the AI sucks at military tactics. Even if they come at you with 10 units, all you have to do is focus on taking out one unit at a time. Without a melee unit, it's impossible to capture a city, so you might want to focus on taking those out first. They will give up pretty soon and beg you for a peace treaty (its funny, actually). You may want to at least build walls in some of your cities in the beginning if someone like Attila is at your doorstep.
3.To outpace the other civilizations, focus on science. Science gives you stronger military units and more buildings to enhance your empire. The base science output comes from population, so food is really important in the beginning. And everyone will tell you, build the national wonder, "national college" as soon as possible. You need a library in every city as a prerequisite to build national college.
4.Happiness is a big deal in this game. You need to make sure you have luxury resources to create happiness, otherwise when your population grows you will get into a state of "unhappiness" which is extremely detrimental to your progress. Happiness is also acquired from other sources such as social policies, religious beliefs and city state allies (mercantile).
5.Beginners usually don't understand how the mechanics works with specialists and citizens. If you build farms and other tile improvements, you don't get any of the resources unless it's being worked by a citizen. You can see where your citizens are working by clicking on your city and expanding the manual citizen control menu. Some of the buildings have slots for specialists. You get big boosts in science, culture, etc from citizens that are placed in those slots (in which case, they are called "specialists")
6.Don't build a monument or an aqueduct, because you get them for free from the tradition social policy tree. Most people max out the tradition tree first for most victory types.