To view your messages and conversations, go to Menu > Messages. You'll be brought to this page:
Click on a message conversation in the left-hand column to view it. Each conversation between you another member will appear in this column. The search bar at the top allows you to search through your previous conversations, and the Gear icon allows you to either Archive a message, or Mark it as Unread.
If you'd like to start a new conversation with a member, click New Message at the top of the column, and add a recipient in the To field. Enter your message in the Type a Message field at the bottom of the screen. If you'd like to include an attachment in your message, click Attach on the right.