In general, your iPhone checks for new messages automatically every 15, 30, or 60 minutes, depending on your preferences (Mail), as well as each time you open the Mail program.
There are two notable exceptions:
Manual checking. You can turn off automatic checking altogether. If, in Settings→Mail→Auto-Check, you choose Manual, then your iPhone won't check for new messages except when you tap the Check button () within the Mail program.
Real-time delivery. If you have a free Yahoo Mail account, you get a delicious perk: real-time email delivery. That's also called "push" email, well known to BlackBerry addicts; it means that new messages show up on your iPhone as they arrive.
There's nothing to turn on here, no options; if you have a Yahoo Mail account, your messages show up as they arrive, automatically. (Yahoo mail, as noted earlier, is also an IMAP account, meaning that when you send, file, or delete a message on your phone, you'll find those changes reflected at Yahoo.com.)
When new mail arrives, you'll know it by a glance at your Home screen, because the Mail icon sprouts a circled number that tells you how many new messages are waiting. You'll also hear the iPhone's little "You've got mail" sound, unless you've turned that off in Settings (Mail).
If you have more than one email account, this number shows you the total number of new messages, from all accounts. The Accounts ...