Trees propagate naturally from seed. Almost every tree – female trees for those species which are single sex – will produce seed each year. The quantity of seed varies from year to year, and how much of it is fertile/viable : this is related to the weather at flowering times and success of pollination.
The exceptions are hybrid trees some of which are infertile and have to be propagated by cuttings, such as the hybrid Cupressus varieties common in gardens. Cuttings are also used for willows and some poplars.
Once seeds are produced by the tree, many, like acorns, hazel nuts, are eaten even before they fall and more go once they reach the ground. Squirrels, mice, birds all rely on the seasonal feast. They also have a more positive role because they help to spread seeds, by eating indigestible hard seeds which are then evacuated in droppings, and also by burying seeds for storage – squirrels and jays are best at this.
Seeds often remain dormant over winter, and need a cold weather spell before they develop. They need warmth and moisture to germinate, light to grow further. Woodland glades and edges, so long as the grassy vegetation is not too thick, are good. A fallen tree creates space, light, and disturbed ground which is ideal for new young seedlings to grow and so eventually take its place.