To setup Gmail in Apple Mail click on Applications and then the mail icon:
If you are not at first prompted to add an account, go to Mail then Preferences, click on Accounts then click on the “+” at the bottom-left corner. The image below shows the add new account screen, to setup your Gmail account we need to be sure and select Google from the options available here:
Click continue, enter your Gmail email address and your Gmail password:
Next, Gmail will ask your permission for Mac OS X to communicate with your Gmail account, click Accept:
The last step is to select the apps you wish to use with your Gmail account.
Check the boxes next to the apps you wish to enable and then click Done.
After completing the steps above you have successfully setup Apple Mail for use with your Gmail email account.