TL;DR: Currently, only from Desktop: Select the Compose Icon > Select Create New Beeper Chat or Create New Beeper Group Chat. Search the contact by username. You can start a chat with another Beeper/Matrix user from Android or iOS yet.

How to start a chat with another Beeper (Matrix) user?

Step-by-Step

From your Beeper Desktop Client

1. Select the compose new message button
   • 
2. Select Create New Beeper Chat or Create New Beeper Group Chat, depending on what you need.
   • 
3. From there, you will be presented with the Direct Messages prompt
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4. Type the username of the other party, this format: @username:beeper.com
   • If you're creating a group chat, you will be greeted with the Create a private room prompt 
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   • Type a name, a topic (if you want one) and select whether you would be making a private or public room. A private room means that only people invited will be able to find this room. This setting can be change later.
5. Once you've filled all required information, you can press Create Room.

You can also chat with Matrix users; how to do so?

Step-by-Step

From your Beeper Desktop Client

1. Select the compose new message button
   • 
2. Select Create New Beeper (Matrix) Chat or Create New Beeper Group Chat, depending on what you need.
   • 
3. From there, you will be presented with the Direct Messages prompt
   • 
4. Type the username of the other party, this format: @username:matrix.org
5. Select your contact and press Go

How to join a Matrix chat?

Step-by-Step

From your Beeper Desktop client:

1. From the Gear icon, select Join Matrix Room

1. Change the server from Beeper.com to Matrix.org.

1. Type the Matrix chat address and join it.