Listing posts with a value in a custom field

Assuming that this meta is for the post type “post” you could create a loop in two ways, get_posts or WP_Query.
I also prefer the meta_query property over the meta_value and meta_key, because it adds the option to add more meta queries quicker as the array already exists.

The get_posts method

$posts = get_posts([
    'post_type'      => 'post',
    'post_status'    => 'publish',
    'posts_per_page' => -1,
    'meta_query'     => [
        [
            'key'     => 'publisher',
            'value'   => 'IBM',
        ]
    ]
]);

foreach ($posts as $post) {
    // your code here
}

The WP_Query method

$posts = new WP_Query([
    'post_type'      => 'post',
    'post_status'    => 'publish',
    'posts_per_page' => -1,
    'meta_query'     => [
        [
            'key'     => 'publisher',
            'value'   => 'IBM',
        ]
    ]
]);

if ($posts->have_posts()) {
    while ($posts->have_posts()) {
        the_post();

        // your code here
    }
}

The best resource for understanding how this works is the WP_Query documentation