This stratagy is for .74 and large map.
As the Byzantines, you are surrounded by challenges and adversaries. To the east there is the Turks, to the north is the Russians, and to the west there are the Magyars and Italy. To survive you must know some things. You MUST build the Hagia Sophia as quickly as possible. Its the only way I've found to keep your economy afloat with expansion and war. The second thing is that your UU isn't good at all for land wars. If you think you rival Basil II, Alexius I Comnenus, Justinian I, and avoid the long decline, read on!
Your Allies
Your main ally will be the Kevian Rus. They will generaly be a monster by the mid to late game. They also will be a great source of tech trading and military assistance. Don't declare war on them.
Armenia is a good ally, but generaly they are too far down on the scoreboard and weak to make a good military ally. But they are good for resource trading.
These will be your main allies. Although if either Poland or Lithuania convert, they are also great allies. Never trust the Magyars!
Your Enemies
They will be many and powerful. Turkey will almost always declare war on you, so keep Constantinople well garisoned! The Germans and French are also threats, Germany more so because of their huge army. The Italians will be an economic threat. They will settle the Balklands and Greece unless your quick about it.
Warfare
The best times for Byzantine warfare are; Late Early Middle Ages, right after knights, and right after foot knights. These are times when quick, decisive armies can easly turn a powerful enemy into new land. Since you will be earning alot of cash hopefuly from the Hagia Sophia, get a load of vassals or swordsman, set slider to zero, upgrade, and you now have a state of the art army ready to attack someone. You MUST defend Constantinople. Not only is it your gold center, if the Turks capture it, their cavalry will pillage every improvement in sight. As long as you hold the city and have an adaquete navy, the Turks arn't getting through.
My recomendations for war order:
Magyars, in the begining they only have alot of spearman.
Turks, they have really nice land.
After that it is either Syria or Europe, you will have a good enough empire for either.
Technology
Since you will be unable to get every tech you want and still be competative, getting to Classical Heritage for trading is critical. A very nice bonus is after Classical Heritage comes Jurisprudence, A very awsome tech. You also don't want to neglect the starting techs.
Economy
This area is reletivly normal, as the Byzantine ecomomy will be very similar to a Cottage Economy, you have alot of nice grassland for it. Also, to build the Hagia Sophia you will need a Great Prophet, as it is the Orthodox shrine. I would recomend getting it through building a church and running a priest specialist. Trying to get the free prophet through Pilgrimage is near impossible above Warlord, as your economy will be too far gone if you manage to get it. It is also a tech I see the AI go for quite early because it enable a civic, wonder, Macemen, and give a GP.
Victory
This is a tough one, I would have to go with New World if you have a large army, or Silk Road if you need a better economy, because the techs along those favor either navy or commerce. Silk Road will be hard unless you have camels, which would entail you invading Syria.
Final Thoughts and Pointers
If you are powerful enough to hurt someone if they invaded you, your are safe for the moment.
You generaly want more cavalry on the western side because you don't have any chokepoints there. Although there should be cavalry and seige engines in Constantinople to counter any seige armies.
Your economy is very fragile, don't overstress it.
So, do you think you can keep the mantel of Eastern Roman Empire, achive the glory of Basil, Alexius, Justinian, and many more, and avoid the humiliating and catastrophic defeat at Manzikert, August 19th 1071?
That is about it for my guide. If you have any problems with it or suggestion, please make your case known.