Pick out a single organism. The lowest level of organization in a biome is the individual organism. For example, a single fish in a marine biome is an example of an organism.
Group organisms of the same type into a population. Thus, all fish in a specific marine biome would be a population.
Add other organisms that are not of the same species, but that interact with the previously defined population. This is called a community, and for fish would include the micro-organisms that they eat, as well as any animals that prey on them.
Add all other organisms (including those that have no relation to the community) and non-organic factors (like water, sunlight and soil) to get the final level of organization in the biome, namely the ecosystem.