wp_query with parameters

Assuming you have variables to hold your custom values for each:

• $category
• $tag
• $author
• $search

Then just create an arguments array, and add keys to it conditionally:

$custom_query_args = array(
    // Set any default args here 
    // NOTE: This is where you'd add
    // things like pagination (posts_per_page),
    // order/sort parameters, and the like
    'posts_per_page' => 10,
    'orderby' => 'date',
    'order' => 'DESC'
);

// If user defines $category, add it
if ( '' != $category ) {
    $custom_query_args['cat'] = $category;
}
// If user defines $tag, add it
if ( '' != $tag ) {
    $custom_query_args['tag'] = $tag;
}

// If user defines $author, add it
if ( '' != $author ) {
    $custom_query_args['author'] = $author;
}

// If user defines $search, add it
if ( '' != $search ) {
    $custom_query_args['s'] = $search;
}

// Run the query
$custom_query = new WP_Query( $custom_query_args );

Note: how you define $category, $tag, $author, and $search is outside the scope of this answer.

Edit

If you want to include a meta query (i.e. custom field) parameter, you can do that as well:

Assuming (user-defined) $post_meta_key and (static) $post_meta_key:

// If user defines $post_meta_value, add it
if ( '' != $post_meta_value ) {
    $custom_query_args['meta_query'] = array(
        array(
            'key' => $post_meta_key,
            'value' => $post_meta_value,
            'compare' => '=',
        )
    );
}