Using the Matrix XMPP Bridge as an End User
If your homeserver has the Matrix XMPP Bridge configured it will pass messages to and from XMPP. You will interact with XMPP by; joining Matrix Rooms specifically bridged to existing XMPP rooms; speaking with XMPP users who have joined public Matrix rooms; or you may use private messaging to speak directly with a specific user in XMPP.
Getting Started
Messaging in public Matrix Rooms
To start, the most basic usage of the XMPP bridge would be to join a Public Matrix room that XMPP users also join to communicate. You or your homeserver administrators will have created a Public room, which XMPP users can search for using a configured endpoint, by default matrix instead of conference.
That's it, by messaging in this room, anyone who is joined from XMPP will be able to see and respond to your messages. As far as how you appear in XMPP, you'll be displayed in room member lists using your Matrix display name, with a full username formatted based on how your homeserver administrators configured. Usually in a format like DISPLAYNAME_HOMESERVER@EXTERNALCOMPONENT.XMPPSERVER, so an example user would look like:
alice_example.com@matrix.xmpp.example.com
In Matrix, XMPP users will appear with Matrix User IDs, following a format like @PREFIX_USERNAME=40XMPPSERVER:HOMESERVER, so an example user would look like:
@xmpp_alice=40xmpp.example.com:example.com
However it's unlikely you will ever need to directly type these, you can use your native clients' functions to interact with users, just like any other Matrix user in Element, or XMPP user in your XMPP client.
Messaging in an XMPP room via a bridged Matrix Room
The alternative to speaking with XMPP users in a public Matrix room they join, is to join an existing XMPP room. To do this all you need to know is the XMPP rooms name and how your homeservers have configured the room name format in Matrix. By default, XMPP rooms in Matrix are translated following a format like #PREFIX_XMPPROOMNAME_CONFERENCE.XMPPSERVER:HOMESERVER, so an example room alias would look like:
#_xmpp_exampleroom_conference.xmpp.example.com:example.com
So you can either enter this in the room search prompt, or simply send /join #_xmpp_exampleroom_conference.xmpp.example.com:example.com in any room (nothing is sent to the room you send this to), for the Element Client to automatically join you to the room.
Once joined, exactly as with public Matrix rooms, you can communicate with anyone else in the room just as you normally would in Matrix.
Private Messaging XMPP Users
XMPP users appear in Matrix as Matrix users, you can view the list of people in a room by clicking the i icon in the top-right of the client, then selecting People. Here you can see all users within the room, including those users created to represent XMPP users. The format for their Matrix User IDs is configured by your homeserver administrator, see above for defaults.
Just like with any other Matrix user; you can click on a person from this pane; click on their profile picture next to any message they've sent within the room; or simply search for them to initiate the DM. Compose your initial message and send to start a Direct Message with the XMPP user. A XMPP user can likewise start a private message with you, using your XMPP username - if they do, you will be invited to a DM just like any other Direct Message.