Private messages are referred to as conversations. To start a conversation click on either messages or the conversations icon in the top horizontal menu. When starting a conversation you may get this error:

Error Message

You have reached your maximum conversations limit and cannot create new conversations.

This means you reached the limit of your conversations quota which is 200, and will need to delete some old conversations.

To delete conversations go to the conversations page (click messages or the conversations icon in the top horizontal menu). At the top right corner you can see a box with the number of active conversations, you need to get this number below 200. To do so go to the last page of conversations (assuming you prefer to get rid of the oldest ones first), and check off all the ones you want to delete. At the bottom right corner a box will pop up showing the number of conversations you selected, click on that and then click leave conversations.

Any other questions about, or issues with conversations/private messages may be posted in this thread.