How do the biotic and abiotic components of an ecosystem interact?
It varies by the ecosystem.
Abiotic factors can be extremely broad. Sunlight, air, soil, rock, minerals, water, etc. are all biotic factors. Sunlight provides energy that plants utilize to grow, which ultimately holds up the whole biotic community of an ecosystem. Air also interacts with plants, helping them grow by providing a source of carbon (CO2) and other nutrients.
In general, abiotic factors like rock, soil, and water interact with biotic factors in the form of providing nutrients. Just as humans mine mountains and cultivate soil, rock and soil provide resources for plants, and plants cycle the nutrients through so they (usually) end up back in the ground where they began. The water, phosphorus, nitrogen, and carbon cycles are examples of this.
Another way biotic and abiotic factors interact is that biotic factors often change the geology and geography of an area. Geologically, organisms create topsoil by breaking down rock layers and dying, which provides detritus with which to form new soil and return nutrients to the ground.
Geographically, plants and animals can directly influence the way rivers flow by preventing erosion at the banks and allowing rivers to flow in straighter lines. On this topic, I highly suggest watching David Attenborough's video on how the wipeout and reintroduction of wolves affected the rivers of Yellowstone: