How do biomes form?
Biomes form by the natural process of colonisation and succession
The question is a little odd, because a biome is a very large area and would usually be expressed as how do communities or (perhaps) ecosystems form.
A biome is defined as 'a large naturally occurring community of flora and fauna occupying a major habitat, e.g., forest or tundra.'
If we start with a bare surface, eg of soil exposed after a landslide or volcanic eruption, then the first organisms to arrive and become established are termed colonisers. By living in this new space, they cause changes to occur which - over time- creates conditions suitable for other organisms to survive. Generally speaking, as time passes, three main changes occur:
the original species present are displaced by later arriving species
the number of species present increases
the biomass (total mass of living tissue) increases.
In different places, with differing climatic conditions, different communities of organisms will form and lead to a climax or stable community, typically forest.