You get new mail and send mail you’ve already written using the Get Mail command. You can trigger it in any of several ways:
Click the button on the toolbar.
Choose Mailbox→Get All New Mail (or press Shift-⌘-N).
If you have multiple email accounts, you can also use the Mailbox→Get New Mail submenu to pick just one account to check for new mail.
Right-click (or two-finger click) Mail’s Dock icon and choose Get New Mail from the shortcut menu. (You can use this method from within any program, as long as Mail is already open.)