Food is constantly used by your Rogue, so you want to try to move through the game as quickly as you can, without going *too* quickly.  It's essentially a delicate balance you must strike.  But basically, if you clear every level of monsters and treasure, and then immediately move on, you should be ok.  Here are some tips, however.

1.  KEEP MOVING! Don't spend any more time on one level than
you have to. Find all the chests (they only appear in rooms), and move
on.

2.  Don't eat food until you're near-starving.  Eat at or near max only if you have encountered lots and lots of food, because doing so will increase your max Belly.

3.  Resting is very useful, but not without its downsides.  Resting spends a bunch of game-turns quickly to heal you up, and so it takes a chunk out of your belly.  Consider just walking around a little bit and then moving on.

4.  There is always a Roasted Food drop in the Genie's level.

With all this said, Food will become easier as our COOK monster and the Item Shop is added.