General:
* Examine
* Scrutinize
* Investigate
* Study
* Assess
* Evaluate
* Dissect
* Break down
* Explore
* Interpret
Formal:
* Decompose
* Deconstruct
* Probe
* Delve into
* Investigate thoroughly
* Subject to critical analysis
Informal:
* Figure out
* Look into
* Pick apart
* Unpack
Specific to particular fields:
* In Science: Test, Experiment
* In Business: Audit, Review
* In Literature: Interpret, Deconstruct
* In Psychology: Assess, Diagnose
The best synonym depends on the specific situation and what you want to emphasize.