After helping a lord win a battle, you will gain reputation with that lord by a few points. Immediately after closing the dialogue with the lord your game will autosave.
Ifyou exit the game without saving and Continue the save from immediately after helping the lord, you will see that the lord is still in the battle you helped with but the enemy army has 0 combatants.
After helping win this easy fight (only send your troops, don't join) you will gain +1 reputation.
You can repeat this process until your reputation with the Lord reaches 100 (Devoted is the highest level, reached at 85). Getting from 0 to 100 takes close to 20 minutes.