Before checking for new messages, make sure you have added your email account to your iPhone or iPad. If you have not, see the tutorial on adding an email account.
Open the Mail app.
Under Mailboxes, tap Inbox.
If Mail starts checking automatically, wait a few seconds. Otherwise, pull down on the message list to refresh it. Mail displays a checking indicator while it looks for new messages.
New messages appear in your inbox. If no new messages have arrived, your inbox remains unchanged.
For automatic message checking, see the tutorial on syncing or fetching email.