You have a few choices. You can use Apple's MFMailComposeViewController class (see below) which allows you to make a message in your app and pass it to iPhone's Mail, without launching the Mail app or leaving yours. You can also implement SMTP in your app to send e-mail directly. You can also hand off your email to a webserver and have the webserver send it out. The easiest is the first way. The drawback is that you don't really know if the message was sent out or not, which depends on whether the network was operational or not and other factors. Of course, if you go with your own SMTP code, you will have to handle all the queuing and retrying in case the network, or server is unavailable, and that means your app has to be running in order to do that.
From Apple's docs:
The MFMailComposeViewController class provides a standard interface that manages the editing and sending an email message. You can use this view controller to display a standard email view inside your application and populate the fields of that view with initial values, such as the subject, email recipients, body text, and attachments. The user can edit the initial contents you specify and choose to send the email or cancel the operation.