To expand on it, I believe we could detect signs of possible biosphere by finding oxygen in the spectral lines of the planet's image. The idea being, free oxygen is highly reactive, and thus can exist in the atmosphere only for brief periods before oxidizing the first thing it bumps into. So, should we find a planet with lots of free oxygen in the air, we either got improbably lucky to catch it before it's gone, or... there is some process on the planet that's actively replenishing it.

On Earth, that process is the biosphere.