Just make sure not to bury the rhizome (horizontal tube that sprouts the leaves and grows the roots). It needs light and water flow around it to stay healthy.
Java fern is a good choice for a new aquarium as it can grow in just about any amount of light. It can grow two ways: by sprouting babies as lauraf said, but also the rhizome will grow in length and add more leaves.
When new plantlets grow from its leaves, it will be older/larger leaves generally. It will look like the leaf is decaying (and it is actually), but don't remove it. You will see small black dots on the leaf and that is where the plantlets will grow from. Once they have developed several leaves of their own and a start of the rhizome and roots, it can be clipped off and moved to its own location if desired.