Gmail is web-based so there will not be a program shortcut on your desktop. You can add a Internet shortcut to your desktop or add a "Favorite" website in your browser.
To add an Internet shortcut on the desktop:
Right Click on the desktop (anywhere in a blank space)
In the popup window, click 'New', then 'Shortcut'
Type the location: https://mail.google.com
Type a name: GMAIL
This icon will take you to the Gmail Homepage so that you can log in.
To change your password in Gmail:
Sign in to Gmail.
Click the gear icon at the top-right of any Gmail page, then Mail settings, and open the Accounts tab.
In the 'Change account settings' section, click Google Account Settings.
In the new window under Personal Settings, click the link 'Changing your Password', enter your current password and your new password