Steem is missing a dedicated internal message system between users.
One option is however to use the memo field of STEEM or SBD tranfers. The transfer memos are plain text and visible to everybody by default, not only to the sender and the receiver. However, memos can also be encrypted in a way that they are only readable by the sender and receiver of the transfer.
Several third party messaging/chat applications are used by steemians
- various Discord channels
- http://forum.steemitforum.com/ (warning unencrypted HTTP, no SSL!)
These applications are not connected to Steem and require a separate sign-up. Users often register accounts with the same username as on Steem.