I just bought a MacBook Air and would like to synch my iPhone email to my MacBook.

BobTheFisherman wrote:

It should sync automatically if the email accounts are configured as IMAP on both devices.

Seconded. Bolded IMAP (which should be default) for emphasis, because your devices will NOT stay synced if the email account is set up as POP3.

To add your email account on your Mac, simply open the Mail app on your Mac and follow the onscreen instructions. Or, go to System Preferences -> Internet Accounts, and add your email account from there.

If you have an iCloud email address, you can enable that for your Mac as well, by going to System Preferences -> Apple ID, signing in, selecting iCloud, and then checking the box for iCloud Mail.

It should sync automatically if the email accounts are configured as IMAP on both devices.