Is it possible to send a private message to another Twitter user without having first followed them?
Or can I send a public message directed at an account without being a follower?
You can send them a public message by posting something with their
@username in it. Everyone can read it.
There are private messages, but you can send those only to people who follow you.
If someone is following you, you can send a direct message from the web via the "message" link on the profile page. Please note: you cannot send a direct message to a user who is not following you.