I know a bit about the Sith War era, which happens to be pre-Old Republic. But, much knowledge really isn't needed. It's effectively still the same as the Old Republic seen in Episodes 1, 2, and 3. Save that there are more Jedi, and far more than 2 Sith.
The Sith have their own Armies, depending on the particular Sith Lord, and there is one Great Lord/Lady of the Sith. The Jedi are much like as seen in the new Trilogy, except that there are a number of seperate enclaves on different planets, like the Enclave found on Dantooine in Knights of the Old Republic. There are a number of smaller Jedi Councils, usually one per Enclave, and one "Grand Council".
There are several different "departments" of the Jedi Order. First, there is the "military" arm, consisting mostly of Knight and Paduwan "Guardians". Qui-Gon Jinn, Obi-Wan Kenobi, Mace Windu, and Anakin Skywalker are examples of Jedi Guardians. Guardians are usually highly proficient in lightsaber combat, tactics, and snubfighter piloting.
Second, there is the more "diplomatic" arm, the beauracracy, the teachers, the diplomats, and the researchers. As in the d20 version of Star Wars, this would consist of a few older "Guardians" and the Jedi "Councilors". Yoda and Palpatine are examples of Councilors, with Palpatine being a Sith Councilor. The Guardians tend to be most proficient in the use of the Force in means other than combat with a lightsaber. Telepathy, foresight, among other force powers are their forte.
Finally, there is the one secret 'order' of Jedi, which are known only to a few privelaged members of the Jedi "Grand Council". They are the Jedi Shadows. As far as the members of the Order know, the Shadows are simply powerful Jedi Guardians. The Shadows are the Secret Police of the Order, meant to hunt down Sith and root out the Dark Side within the Order itself. The Shadow is proficient in lightsaber combat, highly proficient in hand-to-hand combat, and stealth, disguise, trickery, and "dirty" tricks. Some Shadows have been known to completely eschew the use of lightsabers in favor of unarmed combat.