Civ5 is really 3 different games depending on which difficulty tier you're playing at:
Tier 1: From prince on down, you can do whatever you want. You can role-play the history (or an alternate history) of a nation, building the wonders that it built or you think they should have built. Play as aggressive or peaceful as you want as the repercussions of your actions are manageable; there's nothing that the AI civs can do that will disruptyou; maybe cause you to go on a minor tangent, but not disrupt your plans. Or just make an all-powerful nation with every wonder that's two or three eras ahead of everyone else. Overall, the game functions as a blank canvas for you to paint whatever kind of picture you think is attractive, and the other civs are just there to make your masterpiece more perfect. Analogous to: ice cream.
Tier 2: From King to Immortal, the other civs can interfere with your plans, but only if you allow them to. You need to not just do what you want but also be reactive to what's going on around you. Unlike prince level and below, going into a game with an intended victory condition and strategy without seeing the map or who else is on it can prevent you from achieving victory at all. Still, having decent map luck coupled with good strategy will allow you to be the runaway civ by mid-renaissance and snowball ahead of everyone else as the game progresses. A great map and strategy will allow you to be the dominant one even earlier. It's at these levels that employing the exploits... *AHEM* universally beneficial strategies (4-city trad or 6city lib/worker stealing/pre-100NC/education rush/war bribes) solve a lot of your problems, or at least gives you more options to work with Analogous to: a crossword puzzle.
Tier 3: Deity is a different game entirely. Much like a sudoku puzzle has only one correct answer, deity games often can only achieve victory if a certain path is taken, and frankly I've seen quite a few games in which it does not seem that a victory condition could be achieved no matter what route you took. Hope for map luck, hope that AI civs are responsive to some of your actions, hope that you aren't annihilated during certain moments in the game where there is nothing you can do to prevent it, and most of all hope that the guy on the other side of map who you can't interfere with in any way doesn't build a spaceships before you unlock a victory condition. If ALL these things - which you can manipulate and influence but not control - occur, you just might win. analogous to: a jabanero chili contest after a few ulcers.
So, making the leap from tier 1 to tier 2 requires a different mentality but not necessarily a different approach. Instead of going into a game and dictating what happens, observe what's happening around you and adjust for it - don't change your plan entirely, but counter what they do when it threatens you. In single player games, the player always has three advantages over the AI:
1.) Free will. AI's are programmed to respond to certain stimuli in certain ways whereas humans have a choice in their response. Know how the AI will respond and use that response against them.
2,)naval and ranged combat. Quite an exploit, but the AI is just awful at these two things.
3.) Predictability: a spin-off of the first advantage, but the AI is so easy to read, regardless of difficulty level:
-the neighbor who keeps shuffling a large amount of units at your border is going to attack you; regardless of your current diplomatic state.
-the guy with all the wonders is going for a culture victory.
-the guy entering modern before anyone else is in industrial is going for SS
-the guy whose allied with all the CSs is a diplo threat
-the guy who has 4 capitals and eradicated 2 civs is going for domination
