If you sent the message to his "Time line" using the @ symbol before his name, then it will appear in your Timeline (your twitter home page). If he replies to you using and @ reply (called a "mention"), then you can find his message by going to your Twitter homepage and clicking on the tab called "Mentions". That is where you can see everyone who has tweeted using @yourname.

there are two types of reply you can get one is the @ symbol with your twitter name afterwards, and the other is through mail. For mail, you can see a mail shaped symbol on the top of the screen, just click on that.