Minecraft wiki entry for Hunger_management, associated text: The most important point is to avoid taking damage, as healing damage uses far more hunger than almost anything else. This includes not just combat damage, but also damage from falls, fire, poison, drowning, etc.
Armor will sharply reduce damage taken from most causes. Full diamond armor reduces the damage you take by 80%.
Using more powerful weapons will also tend to shorten fights by killing things faster, leaving them fewer chances to hit you. Likewise, ranged weapons can let you kill most mobs with little risk of being hurt.
Especially avoid poison, and try to cure it quickly if you do get poisoned; poison can take a lot of health points, which will eventually need to heal.
Avoid fighting when you can -- 60 blows either way costs as much as healing a point of damage. Taking falling damage does count as a blow.
Avoiding monsters and using a bed at night are the main things here.
Reduce jumping. While mining, carry some cobblestone or logs, and, whenever possible, craft and place stairs, slabs or ladders instead of jumping. 120 jumps cost as much as healing one point of damage.
Avoid sprinting, as it rapidly depletes your hunger bar. Jumping while sprinting is especially energy consuming. Sprinting 60 meters costs as much as healing one point of damage.
Jumping costs four times as much hunger if you are also sprinting, so 30 sprint-jumps equal healing one point of damage.
While crossing deep water, use a boat (or make bridges) instead of swimming, as the former is faster and does not deplete the hunger bar. Swimming 600 meters costs as much as healing one hunger point.