How do I compose a new message on my iPad? I can receive messages (mail) but I don't know how to compose and send a message from my iPad 2...

Gmail and Yahoo mail use a square with a pencil icon which you touch to open to write your message. It may be a universal indicator.

Are you using the iPad's native Mail app or webmail?

If it's the Mail app, then touch the icon that's on the top right hand side of the screen and blank email pane will appear, where you can complete the various addresses and message content.

Tim