Adjusting the style of the auto embed links.

Adding a link to your site from another WordPress site you will very likely get a standard auto embed of the link.
It will look similar to what you see below. (Actually on the frontend it is disabled with the code further below. On the edit post area I can still see it.)

The new WordPress org plugin repository

How do we go about changing this?

Lets take a look at the Html and CSS to see the tags in place for a WordPress site link autoembed. Right click in your browser somewhere in the embeded area and select Inspect Element. The Html and CSS section will then show up below, as can be seen in this screenshot.

Right clicking in the browser and selecting Inspect Element.

The WordPress embed CSS

One can modify the style of the embed to create the embed you want to use.
It will then adjust all the WordPress embeds on your site.

The whole embed:

.wp-embed {
 padding: 25px;
 font: 400 14px/1.5 'Open Sans',sans-serif;
 color: #82878c;
 background: #fff;
 border: 1px solid #e5e5e5;
 -webkit-box-shadow: 0 1px 1px rgba(0,0,0,.05);
 box-shadow: 0 1px 1px rgba(0,0,0,.05);
 overflow: auto;
 zoom: 1;
 }

The embed heading:

p.wp-embed-heading {
 margin: 0 0 15px;
 font-weight: 700;
 font-size: 22px;
 line-height: 1.3;
 }

The embed featured image:

.wp-embed-featured-image.square {
 float: left;
 max-width: 160px;
 margin-right: 20px;
 }

 .wp-embed-featured-image {
 margin-bottom: 20px;
 }

The embed excerpt

.wp-embed-excerpt {

}

The embed footer:

.wp-embed-footer {
 display: table;
 width: 100%;
 margin-top: 30px;
 }

The hidden boxes. 

.wp-embed-share-dialog.hidden {
 opacity: 0;
 visibility: hidden;
 }
 .wp-embed-share-dialog {
 position: absolute;
 top: 0;
 left: 0;
 right: 0;
 bottom: 0;
 background-color: #222;
 background-color: rgba(10,10,10,.9);
 color: #fff;
 opacity: 1;
 -webkit-transition: opacity .25s ease-in-out;
 transition: opacity .25s ease-in-out;
 }

Just go ahead and adjust. If there are sections you want to hide then use display: none; It removes the specific area (CSS class) you added it to.

The code to add to your functions.php file to remove autoembeds:

function disable_embeds_init() {

    // Remove the REST API endpoint.
    remove_action('rest_api_init', 'wp_oembed_register_route');

    // Turn off oEmbed auto discovery.
    // Don't filter oEmbed results.
   add_filter( 'embed_oembed_discover', '__return_false' );

    // Remove oEmbed discovery links.
    remove_action('wp_head', 'wp_oembed_add_discovery_links');

    // Remove oEmbed-specific JavaScript from the front-end and back-end.
    remove_action('wp_head', 'wp_oembed_add_host_js');
}

add_action('init', 'disable_embeds_init', 9999);

It removes the embed from the frontend and backend.

Or use the disable embeds plugin. Github: https://github.com/swissspidy/disable-embeds/blob/master/disable-embeds.php
To have better control of the embeds try out the plugin Embedly.

A very easy way is to actually add a . before the link like so: .https://wordpress.org/support/topic/how-to-disable-auto-wordpress-emmed-script?replies=6
Then create the links. Just as I have done right below. A dot before the link.

Resources:
.https://wordpress.org/support/topic/how-to-disable-auto-wordpress-emmed-script?replies=6

https://crunchify.com/how-to-disable-auto-embed-script-for-wordpress-4-4-wp-embed-min-js/