After you've ignored a person, they are no longer able to send you instant messages or see whether or not you're online. The person will stay on your Ignore List until you take them off, so you don't need to ignore them each time you come online.
To view or edit your Ignore List in the Windows version, click the Messenger menu and choose Edit Ignore List. To do the same in the Java version, click the Edit menu and choose Ignore List. You can choose either to ignore individual users or to ignore all people who are not on your Friend List.