A default setting in your TR profile prevents other users from sending you private messages.
To allow other users to send you private messages, in "My workspace", click on "Edit Profile" and update your "Contacts permissions".
Now other users can send you private messages.
A Private message is sent as an email from the registered email address of the sender to the email address of the recipient.
Note that although the user-id of the sender is visible in the message, there is no straightforward way to open the senders profile on TR, unless the sender includes a link in the message.
And, for the same reason, if a message refers to a discussion thread, then a link to the referred discussion can be very helpful.
If you sent a PM to someone, then the other person may opt to reply in the discussion thread for (at least) two reasons:
1. If the conversation may be useful to other participants in the communication and the contents don't need to be regarded as confidential.
2. In order to not reveal their email address without need.
Finally, note that several members on TR specifically ignore PM from other members if the sender has PM blocked in his own profile.