When you edit a message, at the top of the edit box is a row of square buttons. One of them looks like a signature. When you click on it, it inserts the signature code wherever the blinking cursor is. So, to sign a message, move the cursor to the end of your post and click the sig button. On Wikipedia, it is considered proper "Wikiquette" (WI-kee-ket) to sign your messages on talk pages. This prevents readers from getting your comments confused with those by other users. The default signature for your account is your username, but you can customize it in your preferences menu.
Read more: en:Wikipedia:Sign your posts on talk pages