Archive in Gmail just means that the inbox label has been removed.
Select an email by opening it or checking it, then one of the buttons at the top of the page will allow you to archive the email.
Archiving works best if you have at least one other label on the message. That means that the message can be found under that label. The strength of Gmail is that a message/conversation can have multiple labels. In other systems a message can only be in one folder, but Gmail allows it to be found under multiple labels. The multiple labels can also be used to zero in on the correct set of messages during search.