When the sperm cells find the egg cells, they fuse their genetic material to make a cell with the full adult fern set of genes. This cell is the beginning of the adult fern, located in and protected by the gametophyte structure. As it grows to become the sporophyte, it takes over from the gametophyte and becomes the adult fern. Here is a diagram that shows the fern life cycle. The diagram is adapted from a more detailed one on the Australian National Botanic Gardens website, here .
Ferns can reproduce in other ways, too.
It is possible for a sporophyte to grow from the gametophyte without fertilisation, a process known as apogamy . This can happen in drier areas where there is insufficient water to allow normal fertilisation. Brackens often spread this way. When the parent frond droops and touches the soil, the baby plant takes root on its own. It is a faster method that some ferns use to reproduce mature adult plants, in addition to normal reproduction by spores.