If it wasn't set up properly on the other person's device you'd get an error message in the "Send" line. So if your device's send button is grayed out it sounds like everything may not be set up properly on your device.
Hope that helps and others may chime in as well.
iOS: About Messages
iOS: Troubleshooting Messages
Apple - iOS 5 - See new features included in iOS 5.
Apple - iCloud - Your content. On all your devices.
(iMessage = Page 47)