The easiest way to grow is to eat the little animals that show up in the maze. There are birds, frogs, and little rodent things. As is typical of snake food, they don't have the decency to sit still. The rodents run almost constantly and are nearly as fast as you are. Frogs make short, infrequent hops and aren't inconvenienced by walls.
Birds can fly across the maze without obstruction.
You want to eat the critters for two reasons. Mainly, they're a safe way to add a segment to your own body. Thing is, the game doesn't give you any special favors. If an enemy snake has a snack, it gets the same benefit you do. So eat to prevent the other snakes from growing.