How do I get posts by multiple post ID’s?

You can use get_posts() as it takes the same arguments as WP_Query.

To pass it the IDs, use 'post__in' => array(43,23,65) (only takes arrays).

Something like:

$args = array(
    'post__in' => array(43,23,65)
);

$posts = get_posts($args);

foreach ($posts as $p) :
    //post!
endforeach;

I’d also set the post_type and posts_per_page just for good measure.