Minecraft wiki entry for Hardcore_mode, associated text: Walk and avoid jumping when you are not being pursued by a mob. Sprinting can deplete a lot of your hunger bar if you are not careful.
While walking around, try to punch passive mobs with meat drops to death, such as pigs, which drops porkchops.
Do not jump too much. It takes down your hunger bar if you are not careful. Use stairs and ladders instead of jumping if you are low on food, but it may be hard to find the resources to have many of them.
Try not to take unnecessary damage. The fastest way to lose a full hunger bar is regenerating health.