I think half of what I do as a DBA is "spelunking" - exploring the situation at hand to see what the real problem is. Nine times out of ten, the thing that was presented to me isn't the thing I end up working on.
So where do you start with this process? Well, I normally grab as much info as I can on the situation, and start peeling back the issues to find the root cause. Lots of tools can help you do this, like PBM, the Management Data Warehouse, and even PowerShell, but before I touch the tech I make sure I know just where the issue is. I know, it sounds like the 101 thing to do, but in the heat of the moment it's often too easy to fall back on "doing something" before I really know what to do. I use OneNote a LOT, so I put a troubleshooting checklist in there and I use it religiously.It's saved my bacon multiple times.