Copy the file to a computer that has FileMaker 13 installed on it. Doesn't really mater if this is a Mac or Windows computer.
Select Open From FileMaker's File menu, select your FM 9 file and open it.
This will produce a copy of your file converted to the newer .fmp12 file format.
Test the converted copy to make sure that all works as expected. There shouldn't be many issues in an upgrade from 9 to 12.
There are very few Mac vs. Windows differences to be concerned about. A few that come to mind:
The same text on a Windows machine takes a few pixels more space both horizontally and vertically. So the first time you view a layout created on a Mac on a Windows machine, you may need to enter layout mode and make a few size adjustments so that the text on the field isn't clipped and doesn't wrap to a second line in undesirable fashion.
File paths to files--such as you might use to insert a file into a container field or with an Export Fields or Export Records script, are different on Windows systems when compared to Macs. You might need to do a few updates to correct the issue.
Management of multiple open FileMaker windows is far smoother on a Mac than on a Windows system. You may find that you have to make changes to scripts that open and close multiple windows in order for them to function more smoothly on a windows system in some cases.