Start with running a defrag on the computer. You do this by double clicking on my computer, right clicking the C drive, properties, tools, degragment, defragment now.
This may take a while if you don't do it often. If it has been done in the last week then ignore this.
Afterwards, in the same screen there is an option for Error Checking. Hit Check Now in there. It will not let you do this because it can only work when all the files are available and that will never be true for a C drive when windows is loaded. It will make you schedule it for the next startup. Accept that and restart the computer.
This may again take a long time.
After you do those things, try to shut it down again and see how long it takes.
If it still has problems, then reply back in here that it didn't help and type out the maker/model/approximate age of all the things that are attached to your computer.