2 ways to propagate java fern.
1st way: As mentioned by silly, new ferns will grow from under-side of leaves. The "mother leaf" will produce 2 or 3 plantlets before it begins to die. These can be planted on their own once separrated from the mother plant.
2nd way: The java fern will extend it's rhizome (the large green center root) as it grows. Any section of the rhizome attached to 2-3 healthy leaves may be cut from the rest of the plant to form a new plant.