The Early Game begins in 1095 AD or so, and Alexius Comnenus I is your emperor. The Byzantine Faction or Empire controls a good many territories. There are pluses and minuses to its situation, which must be assessed carefully before you assign tax levels and titles;

Pluses:
1) lots of territory;
2) lots of access to potential ports and trade;
3) lots of potential rebel lands you can conquer and control early on, especially Greece, Bulgaria, Russian Provinces, etc.;
4) Your eventual goal will be to make treaties with the Catholic Powers and destroy the Turks and then the Egyptians and Control the East.
5) You have great generals (Alexius is seven stars) and units (Kataphraktoi) and advanced units. Your smaller forces can defeat other countries bigger forces. However, use bribes and diplomacy when possible to win over forces before attacking. Be a true Byzantine ruler!

The Generalized Strategy in the early game is,

1) destroy the Turks,
2) do not fight more than one faction at a time,
3) build up your trade economy (Constantinople is a HUGE trade income)
4) control all of the ports in Asia Minor before you grasp the interior (the interior will take troops and be expensive to maintain).
4) Rum is a great province, though--once you have it, it generates income and also great units right away.
5) you want the rebel provinces--Greece, Bulgaria, Serbia, Moldavia, on into Russia.
6) You don't want Venice or Sicily camping in Greece on the border of Constantinople. Or Hungary in Bulgaria. So try and conclude treaties with Italy/Venice and with Hungary early. Marry off a princess and use your emissary to bribe a province, then make a treaty with Hungary.
7) avoid the two-front war at all costs. The two front war will arise if you are deep into war with Turkey, don't finish them off, and you get sudden attacks from Italy, Hungary, or a Crusade. It may be wise to delay the onset of war with the Turks until you have put fleets into the adriatic and Ionian seas so as to block any possible attacks from the West by sea. This leaves potential attacks by land from Hungary, so conclude and alliance with them and of course with Italy ASAP.

So Byzantine as a faction has pluses, but it also has minuses.

Minuses:

1) You must control Constantinople at all costs. It is the hugest revenue base, and the largest producer of everything. It can be attacked by land or by sea. Protecting it requires fleets and control of the Black Sea, Aegean Sea and the Straits, as well as a deployment on Constantinople, and eventually, building a fortress there. Eventually troop deployments in Bulgaria as well as in Greece, and in Nicaea.
2) You must avoid a two front war. Do not fight Catholic factions; fight only the Turks and Egyptians at first, and as a rule, do not fight more than one enemy at a time.
3) Crusades can be a pain in the ass as Byzantine. You aren't Catholic, so they need to be allied with you if possible. Make alliance first using your princess with Italy--they are closest--and then with Hungary--and after that, as you get more princesses and emissaries, use one to ally with Poland, Russia (Rus) and Holy Roman Empire. France & England might be fighting. Denmark may ally with you. Aragon or Spain may ally with you. Avoid any alliance with Egypt, Almohad or Turkey because they will be attacked by Crusades. And you will eventually be attacking them too.
4) You don't want Crusades to be hostile to you. Always cede control of a province or territory to a Crusade and then come back later to retake it when you are powerful. NEVER FIGHT A CRUSADE UNTIL VERY MUCH LATER IN THE GAME WHEN YOU HAVE HUGE ARMIES--AND EVEN THEN, PROBABLY DON'T DO IT.
5) You have to fight battles out on in person, you will get higher losses that way. The only exceptions are, don't do that with your King or your heirs, because you might kill them by mistake. That would be very very bad. So autoresolve those.

So that's the lay of the land. For Starters.

Assigning titles; You will have a lot of titles to assign. Be sure you deploy troops as forward as possible defensively towards the Turks. But also use the emissary to bribe one of the rebel provinces to you, and the princess to ally Italy to you. Assign titles to make at least a 3-4 star general on your outer border to supplement Alexius. Don't put Alexius on the front line--he's a backup for when the need arises. He's a star, but don't throw him into battle. Create some 4 or 5 star generals using the resources of Constantinople. It's worth building those buildings that let you confer titles in order to do this.

Taxes; if playing a vanilla game, assign taxes as high as possible while keeping civil order well above 100--keep it above 125 if possible. Keeping troops there will allow more taxes to be levied. Usually as you control provinces, peasant levies can keep order cheaply and allow higher taxes.

Do NOT auto control taxes. Do them individually. Set them low at first. Unless public order is very high, you cant set taxes very high or high except in base provinces. And not until later in the game. But at some point, taxes must rise after you have a province 5 or 10 turns. And if its behind the lines, build farmland and have it produce income. Docks produce trade. Merchants produce trade. Mines produce income.

Navies: BUILD LOTS AND LOTS OF NAVIES. It is critical in the early game to build in this order: a simple fort, a border fort, a town militia, a port, to reduce civil unrest, then a shipbuilding facility to build ships which will only be galleys in early stage byzantine play. This will take a number of turns but it is essential. YOU WILL NEED GALLEYS TO GUARD AGAINST NAVAL ATTACK BY OTHERS. THIS IS THE ONLY WAY TO SURVIVE AS A FACTION. You must guard and own your waters or you will never survive. And, navies bring trade to Constantinople and riches.

Civil Order: You need to build a watchtower, then a guard post (the maximum allowed please) then increase your fortress to a 20 year fortress over time. Add the 5 year addenda for cannons and other defensive materials. Do this first at Constantinople, obviously. Town Keep goes to Town Watch etc. up the ladder. You can build a castle before you build a fortress, so do it. 12 years to a castle, 20 to a fortress.

Specialization: Specialize each province to do one thing really well. This should be obvious if you've ever visited the concept of "Division of Labor". Have each province do what it does well. For example, Trebizond produces Trebizond Archers of note. But it's also on the Black Sea. So build Trebizond Archers until later in the game, then switch to ships.

Armour: You can build armour and metalsmiths to add to the value of your units for offensive and defensive purposes. Also, if you hold any of the lower provinces of Kiev/Rus, an initial armour province let's you build Steppe Heavy Cavalry, a fantastic battle unit.

Conclusion: I was going to do an additional two parts to this discussion, but by now there have proliferated so many online guides and YouTube videos on how to play not just the game but the faction, that it would be superfluous.

Let me conclude by saying, the Eastern Roman Empire lasted from around 330 AD to 1453 AD, and arguably, if you accept Mehmed II's claim of being the Caesar as well as the Sultan, until 1923 AD. That's a pretty long run. The geopolitics of the Ottoman Empire surely resemble nearly 100% those of the Byzantine Empire. Enjoy playing this faction.