Will the tags appear on my post?
What your posts look like depends on the WordPress theme you use.
Some themes show the tags in the posts (say, before or after the post's content).
Most themes don't show the tags in the posts.
For the themes that allow showing tags in your posts, this feature can usually be turned on or off from the theme's settings.
The tags will 100% for sure appear in the backend of a post, when you go to edit it. They will appear on the right-hand-side section, under "Tags".
Also, when you visit your "Posts" section in your WordPress dashboard (your-site/wp-admin/edit.php), you will see the tags of each post next to its title, in the "Tags" column.
Search engines like Google can read and categorize the tags of your posts, even if the tags don't appear for your visitors when they visit your posts.