For mysteries and intrigues and other secret-heavy adventures, here is the process I follow:
1) Take good notes.
2) Compare notes with the other players.
3) If you don't have enough information, come up with a plan to find out the information.
3a. ask nicely
3b. offer a bribe or favor-for-a-favor
3c. eavesdrop
3d. ask somebody else nicely
3e. LIE your damn head off
3f. sneak in and search around
3g. charm person
3h. flattery
3i. taunts
3j. detect thoughts
3k. drag somebody out back and threaten to break their fingers one at a time until they spill the beans <-- Do this one last because it usually causes more problems than it solves
3l. tell the DM that you give up and just need more hints
1) Take good notes.
2) Compare notes with the other players.
3) If you don't have enough information, come up with a plan to find out the information.
3a. ask nicely
3b. offer a bribe or favor-for-a-favor
3c. eavesdrop
3d. ask somebody else nicely
3e. LIE your damn head off
3f. sneak in and search around
3g. charm person
3h. flattery
3i. taunts
3j. detect thoughts
3k. drag somebody out back and threaten to break their fingers one at a time until they spill the beans <-- Do this one last because it usually causes more problems than it solves
3l. tell the DM that you give up and just need more hints