add_action( 'template_redirect', 'wpse149613_form_process' );

function wpse149613_form_process(){
    if(!isset($_POST['submit'])) // assuming you're using POST and submit button name is 'submit'
        return;

    // Validate the form, verify nonce

    // process form

}

<form action="<?=admin_url( 'admin-post.php' ) ?>" method="POST">
    <!-- your inputs -->
    <input type="hidden" name="action" value="myplugin_mycustomaction"/>
    <input type="submit" value="Send"/>
</form>

add_action( 'admin_post_nopriv_myplugin_mycustomaction',array( "class_that_owns_that_function", 'yourmethod' ) );

public function yourmethod()
{
    // Do what you want with $_POST variables
}