Only show content slideshow if “slideshow” custom field exists

You can filter on meta values using query_posts() or a new WP_Query() for example:

query_posts( array(
    'meta_key' => 'slideshow', // the custom field key to check
    'meta_value' => '1',       // the value eg. 0 or 1
    'meta_compare' => '='      // check for equivalence
) );

// your loop goes here

wp_reset_query();

There is a lot more you can do with meta queries if you take a look in the codex including querying on multiple meta keys and values at the same time.