If you're setting up your first email account on your iPhone, simply tap the Mail icon in the dock at the bottom of the home screen. If adding a second or third account, tap Settings, scroll down to Mail, Contacts, Calendars, tap it and then tap Add account…
See also: iPhone Advisor
There's a choice of iCloud, Exchange, Gmail, Yahoo!, AOL, Hotmail, MobileMe and others. Bear in mind that you'll need an email address set up beforehand, as this isn't a way to sign up for a new email account.
If you want to set up a Gmail account, you'd be forgiven for choosing the Gmail option. However, this won't give you access to your contacts, so if you want contacts as well, choose Exchange instead.
In the Email field, enter your full email address. Leave Domain blank.
For Username, enter the first part of your Gmail email address before the @ symbol. Enter your Google Account password in the Password field. [NOTE: If you use Google 2-step verification, you'll need to generate an application-specific password in your Google account settings via a browser first and enter this password here.]
Type Gmail in the Description field, otherwise the account will be labelled Exchange instead.
Tap Next at the top of the screen and then enter m.google.com when the Server field appears. Tap Next again and your account details will be verified. If they're all Ok, you'll see ticks next to each field.
On the next screen you can choose to enable or disable Mail, Contacts and Calendars for the account. Tap Next and the account will be added.
Finally, tap on the new account in the list so you can choose how many days' email to synch and which folders to update via push communication. Most people should leave this set to Inbox.
Push or fetch?
If you want to prolong your iPhone's battery life, disable Push email and enable Fetch instead. This means your phone won't constantly poll the server to find out if there's new email, but will check every 15, 30 or 60 minutes depending on which option you choose. For better battery life, choose the longest interval you can live with.
To see these options, tap Fetch New Data from the main Mail, Contacts, Calendars menu.
Adding unsupported email accounts to the iPhone
If your email provider isn't in the list when you tap Add account… then you'll need to choose the 'Other' option.
Enter your email address, password and a description for the account and tap Next. Select between IMAP and POP at the top of the screen and enter the details for the Incoming Mail Server.