You can only send a direct message to someone who is following you.
In any of the tabs, tap
Tap the text box at the top of the screen, and then enter the name.
As you enter characters, the names of the
Twitter users that match the characters you enter will appear. Tap the name when you see it.
Enter your message, and then tap
You can also send a direct message when you press and hold a tweet of the person you want to send the direct message to, and then tap
Send direct message on the options menu.