If you're looking for a way to add your own buttons, you can write a plugin, as outlined on the WordPress Codex. https://codex.wordpress.org/TinyMCE_Custom_Buttons

The Codex actually links to a full tutorial detailing how to add buttons, and their corresponding shortcodes, as well. http://code.tutsplus.com/tutorials/guide-to-creating-your-own-wordpress-editor-buttons--wp-30182

It's possible to manually add buttons to your editor. https://codex.wordpress.org/TinyMCE_Custom_Buttons

The Codex actually links to a full tutorial detailing the process, as well. http://code.tutsplus.com/tutorials/guide-to-creating-your-own-wordpress-editor-buttons--wp-30182

That will guide you through all the steps:

• Adding shortcodes to your site
• Creating a TinyMCE plugin (register, set up, create buttons, and add what they should do)
• Including editor styles so it displays properly in the admin area
• Including theme styles os it displays properly in the front-end