My java ferns have been making little clones of themselves that are attached to the tips of their leaves. Should I just leave them and eventually they will fall off and plant themselves? Or should I separate them and plant them myself? If so, how do I separate them?

I just let mine fall off and float around.

I s'pose you could just pinch them off an plant them too.

you have to let them stay on as they are until they develop well-defined root structures. Then, when the plantlets begin to look like miniature versions of mature plants, snip off the whole leaf they're on and tie it to a piece of driftwood or rock, making sure the side of the leaf from which the roots sprout is the one in contact with the wood/rock.