The full syntax of the mail() function is:
mail("recipient", "subject", "message", "mail headers");
To add information to the email like the from address you must include this information in the mail headers. For example:
$headers .= "From: $name < $email >\n";
$headers .= "X-Sender: < $email >\n";
$headers .= "X-Mailer: yourdomain.com form\n"; // mailer
$headers .= "X-Priority: 1\n"; // Urgent message!
Replace the variable $name with who you want it to be sent from and $email with their email address. Then use the mail function in the following way.
mail("email to send to", "subject here", "Message goes here", $headers);