Troubleshooting

Hello everyone, as of lately i'm randomly getting freezes when shutting down my pc.

Applications will shut down but then the computer stops responding.

So i have 2 questions for you:
1. Do you know how to solve this issue?
2. What is the troubleshooting process to find the cause of this sort of issues?

I don't want to be fed the answer bu i want to lern how to solve issues by myself.

Thanks to everyone that takes time to answer me. 

What OS are you using?  I had this happen with XP, I never got it fixed, a little while after it started happening I bought some new hardware and upgraded to 7.

Sorry totally forgot to give context;

I'm on Win 7 64bit
i5 3570K -cpu running @ stock clock (3.40GHz)
8gb ram
7970 -gpu