When using a browser:
When in a thread, click on the user's name you wish to send a message to, this will dropdown a menu. Click "Send a private message to..."
Alternatively, you could go to "User CP", which is your user control panel. On the left hand side under the "Private Messages" heading, select "Send New Message". You'll have to type in the name of the user you would like to send a message to in the "Recipient Username(s)" text box.
On our mobile application:
In a thread, tap on a user's avatar, this will bring up their profile. Swipe down and you will fine "Send a Private message".
Alternatively, you could tap on "Messages" found in the menu at the bottom of your screen. Then tap on the icon in the upper right hand corner, looks like a box with an arrow coming out of it. A menu will appear at the bottom of your screen, select "New Private Message". You will have to enter the recipients name in the "To:" box.
Hope that helps.