If you are talking about your e-mail inbox, all the instructions you need for e-mail are in the "E-Mail Help" section under "Site Q&A" (this board).
If you are asking about your Instant Messages, all you have to do is click the delete button at the top right corner of each message to delete that message. Or, if you want to do many at once, put a check mark in the box at the far right end of the message listing (at the top of the IM page) for each message you want to delete and then click the delete button at the top of the listing.
