This is how I do combat maneuvers and make fighters suck less in B/X (or whatever).
When you want to do any sort of combat maneuver, you and your enemy both roll 1d6 + your level/HD. Fighters have a WARRIOR’S INSTINCT which allows them to to add their attack bonus to the roll. If you roll higher than your opponent, you succeed in whatever you were trying to do (within reason, of course).
Fighters can use ADVANCED TACTICS to attempt a combat maneuver while simultaneously making an attack. The success of either is independent of one another, so a Fighter can miss an attack but still do something like disarm their opponent and vice versa. They can do this a number of times per battle equal to their level.