SickCycle
Prince
Instead of answering your question I'm going to just post you links 
I *highly* recommend looking at most if not all of Aelf and Sisiutils games, i also *highly* recommend reading there strategy guides. I added in some extras just to be thorough.
Sisiutils Games: http://forums.civfanatics.com/showthread.php?p=5320091
Sisiutils Strategy Guide for Beginners: http://forums.civfanatics.com/showthread.php?t=165632
Sisiutils Leader Traits: http://forums.civfanatics.com/showthread.php?t=215506
Sisiutils Stack o' Doom: http://forums.civfanatics.com/showthread.php?p=4518097
Aelfs Comprehensive UU Guide: http://forums.civfanatics.com/showthread.php?t=194003
(Aelf also has several games in his sig that you should read, same as Sisiutils)
10 FAQ's Before Declaring War by maltz: http://www.civfanatics.com/civ4/strategy/10faqsdeclwar.php
Triangle Diplomacy by polypheus: http://www.civfanatics.com/civ4/strategy/triangle_diplomacy.php
Monarch Strategy Condensed by eben: http://www.civfanatics.com/civ4/strategy/monarch_condensed.php
Specialization of Cities by iwas: http://www.civfanatics.com/civ4/strategy/specialization.php
I will say this, in order to progress you have to learn how to leverage your leaders abilities, if you look through the strategy guides I posted for you it will all be explained in detail.
As you go up in levels the AI will start to get bonuses to research, production, city maintenance, all kinds of things but keep in mind that the AI's biggest weakness is warfare. I don't know if your much of a warmonger but if your having trouble it's something to think about.

I *highly* recommend looking at most if not all of Aelf and Sisiutils games, i also *highly* recommend reading there strategy guides. I added in some extras just to be thorough.
Sisiutils Games: http://forums.civfanatics.com/showthread.php?p=5320091
Sisiutils Strategy Guide for Beginners: http://forums.civfanatics.com/showthread.php?t=165632
Sisiutils Leader Traits: http://forums.civfanatics.com/showthread.php?t=215506
Sisiutils Stack o' Doom: http://forums.civfanatics.com/showthread.php?p=4518097
Aelfs Comprehensive UU Guide: http://forums.civfanatics.com/showthread.php?t=194003
(Aelf also has several games in his sig that you should read, same as Sisiutils)
10 FAQ's Before Declaring War by maltz: http://www.civfanatics.com/civ4/strategy/10faqsdeclwar.php
Triangle Diplomacy by polypheus: http://www.civfanatics.com/civ4/strategy/triangle_diplomacy.php
Monarch Strategy Condensed by eben: http://www.civfanatics.com/civ4/strategy/monarch_condensed.php
Specialization of Cities by iwas: http://www.civfanatics.com/civ4/strategy/specialization.php
I will say this, in order to progress you have to learn how to leverage your leaders abilities, if you look through the strategy guides I posted for you it will all be explained in detail.
As you go up in levels the AI will start to get bonuses to research, production, city maintenance, all kinds of things but keep in mind that the AI's biggest weakness is warfare. I don't know if your much of a warmonger but if your having trouble it's something to think about.