Gutenberg blocks are the most convenient way to insert a tag cloud. Before the upcoming WordPress version 5.0 is out, you will need to install the Gutenberg editor separately. Please be aware that the Gutenberg plugin is still under development and many features are not yet complete.
On the post or page edit screen, click on the “plus in a circle” icon and search for “tag cloud”. After you inserted the block, select it by clicking once into it. You will notice that in the right side bar (the “Inspector”) you find now (almost) all options that are also available in the shortcode.
In fact, Gutenberg blocks and shortcodes render exactly the same. In the blocks, however, you can often select available options from a list, while for the shortcode you would have to look up IDs and slugs and compile them to lists.
Transforming Blocks to Shortcodes
If you want to switch back from Gutenberg to the classic editor, you need to transform your Tag Groups blocks to shortcodes. You find this feature in the menu directly at the top left corner of the block.
Not yet in Widgets
Gutenberg blocks are not yet available for widget sidebars. We have to wait for WordPress to provide the environment.
Examples of tag clouds are available here.