Openstack offers many well-documented RESTful APIs for request-based programming. However, I couldn't find any information on what URL I should send the HTTP requests for each API. Where am I supposed to send the requests to? Do I need to set up a server myself? How am I supposed to do that? I have a fully operational Openstack running on a local cluster and I can run commands with the CLIs normally.
These questions seem so silly they're not even answered clearly in the docs.
The API endpoints should be viewable through Horizon + the CLI. In Horizon you'll find this information under "Access and Security" > "API Access."
Through the CLI you can find the information via the OpenStack or Keystone client. The client you will use depends on which version of OpenStack you are using. If you are using a newer version then you will probably operate through the OpenStack client.
openstack endpoint list --long
or
keystone endpoint-list
After you get the URLs you should be able to curl them, however they will require authentication. You'll need to auth/get a token from Keystone.