Search posts with custom advanced search form

I’m trying to create a custom advanced search form for my posts. I have been able to create the looks of the search form:

https://i1164.photobucket.com/albums/q575/Tako_Wako/Schermafbeelding2014-03-17om225800.png

As you can see, I want a search form with a search field, dropdown menus and checkboxes. But right now it’s not working correctly. I’m new to WordPress and PHP so all I’ve got I got from the internet.

<?php $provincie = array(
     'hierarchical'       => 1,
     'parent'             => get_cat_id('Provincie'),
     'show_option_none'   => ('Alle Provincies'),
     'hide_empty'  		  => 0 ,
     'order'              => 'DESC' );
    ?>

    <?php $jaar = array(
     'hierarchical'       => 1,
     'parent'             => get_cat_id('Jaar'),
     'show_option_none'   => ('Alle Jaren'),
     'hide_empty'  		  => 0 ,
     'order'              => 'ASC' );
    ?>

    <?php $dag = array(

    	'hierarchical'       => 1,
    	'parent'             => get_cat_id('Dag'),
    	'show_option_none'   => ('Alle Dagen'),
    	'hide_empty'  		 => 0 ,
    	'order'              => 'ASC' );
    ?>

    <?php $activiteit = array(
    	'child_of'                 => 58,
    	'orderby'                  => 'ID',
    	'order'                    => 'ASC',
    	'hide_empty'               => 0,
    	'hierarchical'             => 1 );
    ?>

    <form method="get" id="searchform" action="<?php bloginfo('url'); ?>/">
      <div>
        <input type="text" value="<?php the_search_query(); ?>" name="s" id="s" placeholder="Zoekterm" />
        <?php wp_dropdown_categories($provincie); ?>
        <?php wp_dropdown_categories($jaar); ?>
        <?php wp_dropdown_categories($dag); ?>
        <input type="hidden" id="my_search" name="my_search" value="c_search" />

        <div><h3>Activiteit</h3></div>
    	<div>
    		<?php
    		$categories = get_categories( $activiteit );
    		$checkboxes = '';
    		foreach($categories as $categorie) :
    			$checkboxes .='<input type="checkbox" name="tag[]" value="'.$categorie -> slug.'" id="categorie-'.$categorie->term_id.'" /><label for="categorie-'.$categorie->term_id.'">'.$categorie->name.'</label>';
    		endforeach;
    		print $checkboxes;
    		?>
    	</div>

        <input type="submit" id="searchsubmit" value="search" />
      </div>
    </form>

Can someone point me in the right direction? What am I missing? Or is there an easier way to do this?