How does the CA show it trusts an entity?

They issue certificates. Once they have satisfied themselves that an entity is genuine and trustworthy, they create a certificate as described above, containing the entity's public key, and the entity's identity details such as name, location, DNS host name, etc. They send this certificate to the entity to store, and keep a copy themselves.

The CA generally has a server dedicated to this function, and this machine is also known as the CA.

You can configure your SSL software to compare a received certificate to a list of known trusted CAs. As described above, you can also have your SSL software display a certificate on your screen for you to check the details.