Anonymous Postings

you can use plugins fro the front-end posting:

• Post From Site
• uCan Post
• WP User Frontend

Or you can create the form yourself

    <!-- New Post Form -->
<div id="postbox">
<form id="new_post" name="new_post" method="post" action="">
<p><label for="title">Title</label><br />
<input type="text" id="title" value="" tabindex="1" size="20" name="title" />
</p>
<p><label for="description">Description</label><br />
<textarea id="description" tabindex="3" name="description" cols="50" rows="6"></textarea>
</p>
<p><?php wp_dropdown_categories( 'show_option_none=Category&tab_index=4&taxonomy=category' ); ?></p>
<p><label for="post_tags">Tags</label>
<input type="text" value="" tabindex="5" size="16" name="post_tags" id="post_tags" /></p>
<p align="right"><input type="submit" value="Publish" tabindex="6" id="submit" name="submit" /></p>
<input type="hidden" name="action" value="new_post" />
<?php wp_nonce_field( 'new-post' ); ?>
</form>
</div>
<!--// New Post Form -->

and process it

   if( 'POST' == $_SERVER['REQUEST_METHOD'] && !empty( $_POST['action'] ) &&  ($_POST['action']== 'new_post')) {

    if (isset ($_POST['title'])) {
        $title =  $_POST['title'];
    } else {
        echo 'Please enter a title';
    }
    if (isset ($_POST['description'])) {
        $description = $_POST['description'];
    } else {
        echo 'Please enter the content';
    }
    $tags = $_POST['post_tags'];

    $new_post = array(
        'post_title'    => $title,
        'post_content'  => $description,
        'post_category' => $_POST['cat'],  
        'tags_input'    => $tags,
        'post_status'   => 'draft'
    );
    wp_insert_post($new_post);  

}

And make sure to check for nonce and sanitization of the form fields.

UPDATE

According to your gist code and comment change your function to this:

 if( 'POST' == $_SERVER['REQUEST_METHOD'] && !empty( $_POST['action'] ) && ($_POST['action']== 'new_post')) {
        $has_errors = false;
        if (isset ($_POST['title'])) {
            $title = $_POST['title'];
        } else {
            echo 'Please enter a title';
            $has_errors = true;
        }
        if (isset ($_POST['performer'])) {
            $performer = $_POST['preformer'];
        } else {
            echo 'Please enter a performer';
            $has_errors = true;
        }
        if (isset ($_POST['composer'])) {
          $composer = $_POST['composer'];
        } else {
            echo 'Please enter a composer';
            $has_errors = true;
        }
        if (isset ($_POST['tablature'])) {
            $tablature = $_POST['tablature'];
        } else {
            echo 'Please enter the content';
            $has_errors = true;
        }
        $tags = $_POST['post_tags'];
        if (!$has_errors){
        //save <title>  by: <preformer>
        $title .= " by: " .$performer;

        //save Composed by: <composer> Performed by: <performer> <tablature>
        $content = "<h4>Composed by: ". $composer."</h4><br/><h4>Performed by: ".$performer."</h4><br/>".$tablature;

        $new_post = array(
            'post_title' => $title,
            'post_content' => $content,
            'post_category' => $_POST['cat'],
            'tags_input' => $tags,
            'post_status' => 'draft'
        );
        $pid = wp_insert_post($new_post);


        //save email and submmiter as post meta in custom fields
        update_post_meta($pid, 'submiter_email', urldecode($_POST['email']));
        update_post_meta($pid, 'submiter_name', urldecode($_POST['submitter']));
    }
}