This boss has several main abilities, although most of them are not used when soloing. The ability he does use is Fel Fireball, which leaves a nasty dot on the player that needs to be dispelled.
With that said, the main challenge of this boss is actually dealing with the adds that spawns. Lord Jaraxxus will either spawn 1 Mistress of Pain, or 3 Felflame Infernals. The first add will always be the Mistress of Pain.
Since Mistress of Pain hits just as hard as Jaraxxus himself, it is a good idea to use the T13 4pc bonus to burn it down asap. 3 Felflame Infernals will then spawn a short while later, and those are a lot easier to deal with. Just place a VT and SW:P on each of them and they will die.
Mistress of Pain will spawn again, and this time 4pc T13 is no longer an available option. Therefore it is much harder to survive. To deal with the second Mistress of Pain, run far away from the nether portal beforehand, and as she appears, quickly put all three dots up followed by a Dispersion before she lands any damage. Once Dispersion wears off, quickly burn off her remaining health and hope for the best. After surviving past this point, victory is pretty much guaranteed as the next set of adds are going to be the infernals again, which are easy to deal with, followed by another mistress which can be dealt with using T13 4pc since it will be up again.
The boss himself should pretty much be dead by that point.