I don't have my own web site. I understand how to share images, but I'd like to share the gallery that I can create on Lightroom. How can I do that? Does my CC monthly contract allow me to create a web site through Lightroom CC? Or can I use Flickr or Shutterfly?
Take a look at Adobe Portfolio which is part of your CC subscription and allows you to use the synced images in a web site format. You can point it to your own domain, if you have one.
This is a simple "shrink-wrapped" solution. If it's not enough, you would need to get your own web site and learn enough HTML to integrate the LR-produced web galleries in it.