You need to run the Blender executable from the command line.
In Windows this requires you to run a new Command Prompt and the execute blender.exe from the correct location.
In Linux/MAC the process is similar.
On my Windows machine, I go to the Start Bar and type in Command
in the new window I type the directory to where Blender was installed followed by the program I want to run, blender.exe
To capture all the output a redirection character > is used.
Finally I have a folder on my C: drive called "tmp" that I know I have access to write to. You will have to enter a folder and filename your Windows user can write to.
After running Blender the new file myfile.log has the following contents. This was after simply opening and closing blender. (type is a windows program that just dumps text files to the console)