I found this tutorial from Google really useful when you want to create new Gmail account for your Apple Mail application.
Step 1. Mail ▸ Preferences…
Step 2. Accounts ▸ Add New Account
Fill in your name, full Gmail address and your Gmail password. It will look like image below.
Step 3. Incoming Mail Server
Select IMAP as your account type and use
imap.gmail.com as your incoming mail server.
Step 4. Outgoing Mail Server
smtp.gmail.com as your outgoing mail server and use your correct Gmail address and password for authentication.
Step 5. Summary
Read the summary and click on create to confirm your creating new account.
Now you can see your new Gmail account has been added to your Apple Mail Accounts.