Uploading avatar from the frontend

You only need to of these hooks show_user_profile to show the extra fields and personal_options_update to update, try:

<?php
ob_start();
include_once("../../../wp-load.php");
get_header(); 

/* Get user info. */

global $current_user, $wp_roles;
get_currentuserinfo();

/* Load the registration file. */
require_once( ABSPATH . WPINC . '/registration.php' );

/* If profile was saved, update profile. */
if ( 'POST' == $_SERVER['REQUEST_METHOD'] && !empty( $_POST['action'] ) && $_POST['action'] == 'update-user' ) {

    /* Update user password. */
    if ( !empty($_POST['pass1'] ) && !empty( $_POST['pass2'] ) ) {
        if ( $_POST['pass1'] == $_POST['pass2'] )
            wp_update_user( array( 'ID' => $current_user->id, 'user_pass' => esc_attr( $_POST['pass1'] ) ) );
        else
            $error = __('The passwords you entered do not match.  Your password was not updated.', 'profile');
    }



    /* Update user information. */
    if ( !empty( $_POST['url'] ) )
        update_usermeta( $current_user->id, 'user_url', esc_url( $_POST['url'] ) );
    if ( !empty( $_POST['email'] ) )
        update_usermeta( $current_user->id, 'user_email', esc_attr( $_POST['email'] ) );
    if ( !empty( $_POST['first-name'] ) )
        update_usermeta( $current_user->id, 'first_name', esc_attr( $_POST['first-name'] ) );
    if ( !empty( $_POST['last-name'] ) )
        update_usermeta($current_user->id, 'last_name', esc_attr( $_POST['last-name'] ) );
    if ( !empty( $_POST['yim'] ) )
        update_usermeta($current_user->id, 'yim', esc_attr( $_POST['yim'] ) );
    if ( !empty( $_POST['description'] ) )
        update_usermeta( $current_user->id, 'description', esc_attr( $_POST['description'] ) );

    //extra fields (simple local avatars ....)
        do_action('personal_options_update', $current_user->id);

    /* Redirect so the page will show updated info. */
    if ( !$error ) {


header("Location: ".$_SERVER['PHP_SELF']);

        exit;
ob_flush();
    }
}
?>


        <div id="post-<?php the_ID(); ?>">
            <div class="entry-content entry">
                <?php the_content(); ?>
                <?php if ( !is_user_logged_in() ) : ?>
                        <p class="warning">
                            <?php _e('You must be logged in to edit your profile.', 'profile'); ?>
                        </p><!-- .warning -->
                <?php else : ?>
                    <?php if ( $error ) echo '<p class="error">' . $error . '</p>'; ?>
                    <form method="post" id="adduser" action="<?php the_permalink(); ?>">
                        <p class="form-username">
                            <label for="first-name"><?php _e('First Name', 'profile'); ?></label>
                            <input class="text-input" name="first-name" type="text" id="first-name" value="<?php the_author_meta( 'user_firstname', $current_user->id ); ?>" />
                        </p><!-- .form-username -->
                        <p class="form-username">
                            <label for="last-name"><?php _e('Last Name', 'profile'); ?></label>
                            <input class="text-input" name="last-name" type="text" id="last-name" value="<?php the_author_meta( 'user_lastname', $current_user->id ); ?>" />
                        </p><!-- .form-username -->
                        <p class="form-email">
                            <label for="email"><?php _e('E-mail *', 'profile'); ?></label>
                            <input class="text-input" name="email" type="text" id="email" value="<?php the_author_meta( 'user_email', $current_user->id ); ?>" />
                        </p><!-- .form-email -->
                        <p class="form-url">
                            <label for="url"><?php _e('Website', 'profile'); ?></label>
                            <input class="text-input" name="url" type="text" id="url" value="<?php the_author_meta( 'user_url', $current_user->id ); ?>" />
                        </p><!-- .form-url -->
                        <p class="form-yim">
                            <label for="yim">yahoo</label>
                            <input class="text-input" name="yim" type="text" id="yim" value="<?php the_author_meta( 'yim', $current_user->id ); ?>" />
                        </p><!-- .form-yim -->
                        <p class="form-password">
                            <label for="pass1"><?php _e('Password *', 'profile'); ?> </label>
                            <input class="text-input" name="pass1" type="password" id="pass1" />
                        </p><!-- .form-password -->
                        <p class="form-password">
                            <label for="pass2"><?php _e('Repeat Password *', 'profile'); ?></label>
                            <input class="text-input" name="pass2" type="password" id="pass2" />
                        </p><!-- .form-password -->
                        <p class="form-textarea">
                            <label for="description"><?php _e('Biographical Information', 'profile') ?></label>
                            <textarea name="description" id="description" rows="3" cols="50"><?php the_author_meta( 'description', $current_user->id ); ?></textarea>
                        </p><!-- .form-textarea -->
                        <?php do_action('show_user_profile',$current_user->id); ?>
                        <p class="form-submit">
                            <?php echo $referer; ?>
                            <input name="updateuser" type="submit" id="updateuser" class="submit button" value="<?php _e('Update', 'profile'); ?>" />
                            <?php wp_nonce_field( 'update-user' ) ?>
                            <input name="action" type="hidden" id="action" value="update-user" />
                        </p><!-- .form-submit -->
                    </form><!-- #adduser -->
                    <?php endif; ?>
                </div><!-- .entry-content -->
            </div><!-- .hentry .post -->
            <?php comments_template( '', true ); ?>