To get a logcat, you first need adb on your PC. Search Google for how to find and install that. Once it's installed, I believe you need to open up a cmd window to run it, as it's a command-line tool.
Now, connect your phone to your PC and run "adb logcat". It will dump the buffer and continue to print messages as they are generated.
Or you can run eg. "adb logcat -d > logcat.txt" to dump the buffer to a file named logcat.txt.
There will be lots of data. You can probably find tools to search through it for particular strings. Even notepad should work for simple stuff.