By fighting in battles you gain Experience. Experience can be spent to raise your skills and abilities in exactly the same way as when you create your character. To raise an ability or skill simply spend points equal to the new level of the ability or skill and mark the change on your character sheet. Once spent points are gone and cannot be restored.
If you do not win enough experience from a battle to raise an ability or skill, or you do not wish to do so, then note the spare points on your character record. You can save them for as long as you like, and nothing can make you lose these points other than spending them.
You can also gain experience by going to the Quintain.