General:
* Examine
* Scrutinize
* Investigate
* Study
* Dissect
* Evaluate
* Assess
* Interpret
* Break down
* Probe
More specific:
* For data: Process, interpret, explore, chart, model, categorize, classify, quantify
* For a problem: Diagnose, troubleshoot, debug, identify, resolve
* For a situation: Decompose, unpack, explore, understand, decipher
More informal:
* Look into
* Figure out
* Take apart
* Pick apart
The best synonym will depend on the specific situation you're using it in.