Yes, you need to be following that person. At the top at Twitter.com, click Me to go to your profile. On your profile, there is your name and your avatar, and below that a button that says Edit profile with to the left of it a button with an envelope. Click that, then click the New message button in the popover that has opened. You can now type the name of the person you want to message, and the message you want to send below that.