If someone tweets you directly or you see a tweet that you wish to respond to you can reply to it. This allows you to develop relationships with people whilst improving your reputation and brand on twitter.
To reply to a tweet find it and at the bottom of the tweet you will see the option to ‘reply’, simply select this. You will then see a box appear below the tweet the handle of the creator of the tweet. Simply create your message and select ‘Tweet’. Its that simple.