To do this you need the Legacy of Rome DLC, and in full disclosure I used the Leader Creator DLC also. That said, my advice will help you either way.
The Turkish Invasion and Unruly NoblesEdit
If you have never played as the Byzantines, it is important to know that you start out as soon as possible, as I do, then you will be starting with a war on your hands. The Seljuk Turks are invading Armenia, and have a large army on your border with which to do it. If you let this overwhelm you, as it did me the first time, you won't have a good time. While the army is composed of levies, it feels like Mongol Horde. What you need to do at this point is gather all of your levies, and place them near your enemy, but keep running away. The terrain shouldn't be able to support the invaders, so they will start falling to disease. This is critical, because you will not be able to win in an outright battle until their numbers are lowered.
I tried. It didn't work. Instead, I lost a lot of war score and had to start over. Once you crush the invading army, merely reclaim the areas that suffered successful seiges by the enemy, and start beseiging the enemy. It should only take a few for the Persians to agree to a draw, if not a surrender. At this point, the easy part is over.
As soon as the war with the Turks is over you are going to have a civil war. Why? Because the war with the Turks gave you a plus 30 likeness for "defending against infedels". As soon as that is gone, your vassals remember that your personal diplomacy is low, you are a foreigner (while Greeks are the dominant group in the Empire, there are many Armenians and Balkan peoples in your Empire), and the crown autorithy is usually medium or above.
If you can afford it, try assassinating the leader of the rebellion. If that doesn't work, then focus your troops against the leader of the rebellion, for whatever reason his holdings count for more towards the war score. If necessary, you can lose the war- assuming it is just a matter of crown authority. You always have to remember that while you are fighting yourself, your enemies can pick off your peripheral rebels. Is it really worth getting more levies, just to have to reclaim territory later?
Pushing the Advantage and Thwarting the CrusadeEdit
Shortly after the failed invasion of Armenia, the Seljuk Turks should collapse into a succession crisis or civil war. At this point, I would recommend fighting all of the Turkish rebels as rapidly as you can. Remember, you get to hand out the captured territory to loyal followers. Always pick people of your culture and religion, and always pick people with either the content trait or gregarious trait. Content people will almost always stay loyal, and gregarious people will turn the Turks into Greeks... eventualy. Now that you have expanded, I would recommend a few years of peace. Let the "raised levy" subtractor go down a bit, and then, when you feel confident, start an aggressive war against Egypt. I personally went after the coast, because I could send troops by boat rather than waste time walking to the enemy. The coast has an added advantage: It's the path to Jerusalem.
At some point the Pope will call his crusade. At this point, I would recommend laying off Egypt, and allow them to fight off the Catholics. From my experience, despite the historical record, the 1st crusade almost always fails, and you want it to. Remember, Jerusalem is a kingdom, not a dukedom, and once the Catholics have it, who is to say they will be friendly? During the Crusade you might try expanding deeper into the Caucaus region, or grabbing some more Balkan territory, or both. Once the Crusade is done, fight Egypt again. It is likely that their King will be old, so one war can quickly lead to another once he dies. Do your best to grab all of the dukedoms of the Kingdom of Jerusalem, and then you will never have a Catholic problem on that side of the world again. In my game, the next Crusade was launched against Andalusia.
Once you have made it that far, you are pretty much set for the rest of the game. The key is to continuously groom a worthy heir, which can sometimes mean your grandchild instead of your son. Also, don't be afraid to let your daughter inherit, just make sure she marries matrilinealy. The first ruler of my Roman Empire was an Empress. With Egypt and the Turks weakened, you can begin to reclaim the territory necessary to reconstruct Rome. Never stop invading Egypt and the Turks, because they will always be ready to pounce on you when you are weak. That doesn't mean breaking truces, but it does mean thinking of where you are going to invade once the truce is up.
Anyway, I hope this helped you are your quest for Imperial Glory.