Where does Ansible need to be installed, and how do you install the community version on a RHEL control node?

Only on the control node: sudo dnf install ansible-core. Managed hosts don't need Ansible installed.

[user@controlnode ~]$ sudo dnf install ansible-core

This gives you the standard commands such as ansible and ansible-playbook. On other systems the same package is available through pip (pip install ansible-core) or the distribution's package manager.

Managed hosts get nothing Ansible-specific. They only need a way for the control node to connect (SSH or WinRM) and, depending on the modules used, an interpreter such as Python or PowerShell. This is the agentless model in practice: install once, centrally.

Go deeper:

• Installing Ansible (official docs) — control node vs managed node requirements and installation options.
• Ansible 101 - Episode 1 - Introduction to Ansible (Jeff Geerling) — installs Ansible on a control machine and runs it against servers live.