Alert runs just fine in DOSBox.
You can download the ISOs for the game from EA (who bought out Westwood in 2002 or 2003). http://www.ea.com/redalert/news-detail.jsp?ncc=1&id=62
You should mount both ISOs at one time, and then switch with CTRL-F4 when the game asks you. For example, I've got these two commands in my AutoExec: mount c ~/emulators/dos imgmount d ~/emulators/CD1_ALLIED_DISC.ISO ~/emulators/CD2_SOVIET_DISC.ISO -t iso -fs iso