Formal:
* Infer
* Conclude
* Reason
* Derive
* Elicit
* Extrapolate
* Surmise
Informal:
* Figure out
* Work out
* Understand
* Realize
* See
More specific:
* Discern (to perceive or recognize something)
* Ascertain (to discover with certainty)
* Uncover (to reveal or expose)
The best synonym will depend on the specific meaning you are trying to convey.