There are at least two ways to do this. The first way is to use your desktop email program, like Outlook or Apple Mail. If you change your Gmail settings to allow POP or IMAP access, you can check Gmail from your desktop mail program to check your Gmail account, too.
If you have no idea how to configure your desktop mail program, don't worry. The second and easier way to check Gmail when offline is to download the browser extension Google Gears. Gmail can use this extension to let you see your Gmail messages right from your browser window, even when your computer is not connected to the Internet.