Welcome to the JavaRanch, Ed. Your question doesn't have much to do with IO in particular, so I'm going to move it to Java In General, Beginner. In the mean time, you may want to give us some more details on your assignment. Do you just need a username/password dialog? A finite state machine simulating an ATM? Exactly what do you have a problem with? What have you tried? Can you share some code with us?
How about first stating what your ATM stands for? The teller to withdraw cash from? Or something to do with the network stuffs (Asynchronous Transfer Mode)?
And, for your application, is it going to be a desktop application that probably uses RMI? Or is it going to be a web-application? There're some differences in the actual implementation for a simple login in both situations.
Nevertheless, you would require a database to store your User Ids & encrypted password pair for authentication. You've to decide on what hashing/encrypting algorithm to use for your password & where to look for such implementations (try Googling).