The public @ message
Type @ followed, without a space, by the person’s name: @loosewire
This message will appear in their @replies section of their account that there is a message for them. (And they may get an email message depending on the notification settings of their account).
(You can also reference someone without using the @ sign, but unless they’re checking for all tweets that include their name, chances are they’ll miss it.)
The public reply
Move your mouse over the blank space to the immediate right of a tweet.
Click on the reply arrow.
At the top the status box will have changed to a reply box and the person’s twitter name will have been entered prefaced by the @ sign:
[...] Messaging via Twitter: Public [...]