Time has a funny way of slipping by unnoticed while playing Civ...
Interestingly, your first several games will be the longest ones as you learn how to get through the tech tree more efficiently as you learn more about the game. Even so, though, civ games aren't like starcraft games, where you can just play a few games over an hour. Playing a game of civ takes several days unless you get super addicted, as it's probably, idk, 8ish hours of gameplay per game on standard speed? Maybe a little more? It also depends on what you do in the game, since you'll have more to do over the course of turns if you're involved in a lot of wars, or have to worry about constantly spreading religion.
Enjoy civving! I hope you enjoy the game, and welcome to the forums!
Varies a lot depending on how deep you want to go in on strategy and micro-management.
I've played a standard paced game in a 8-ish hour timespan, but that was without really going in to my cities every few turns and reassigning my citizens to work the best tiles/slots.
I'd imagine if this is your first civ game, you wont be doing too much micro-management but since you won't be familiar with the tech tree, nor will you be playing particularly optimally, the game could take longer since you'd be a little behind.
So basically I have no idea how long it will take you, but I'd imagine between 5-15 hours, likely closer to 15.
EDIT: Welcome to civfanatics!
You have options for how long or short you'd like to game to be before you start. I'd recommend playing your first couple of games on standard speed, which usually takes me at least a couple of solid evenings of play time. I personally prefer marathon, however, in which case I'll regularly have games that last two weeks or more. As for my longest, I couldn't really say. Time has a funny way of slipping by unnoticed while playing Civ...
This. This is so true. Civ is by far the most addicting video game I've ever played.
There's also the possibility for a game like this one: http://www.cnn.com/2012/06/18/tech/gaming-gadgets/civilization-ii-ten-years/
Probably unlikely though
You can finish the game in 3 hours or less if you've picked less than 5 Ais. Late game turn times are horrendously long. That's why I usually play against 2-7 other AIs.