This article explains how to save an email to a folder. Instructions apply to Gmail, Outlook Mail, Yahoo!, Mail.com, and AOL Mail.
Most email providers will let you simply drag the message directly into the folder of your choice. Others that don’t support drag and drop will likely have a menu you can open to move the message elsewhere. This applies to both online clients and downloadable clients.
For example, with Gmail and Outlook Mail, in addition to dragging and dropping, you can use the Move To menu to select an appropriate folder to move the message to. Yahoo! and Mail.com work similarly, except that the Move menu is simply called Move. With AOL Mail, it's in the More > Move To menu.
Most providers allow you to move emails into folders in bulk, so you don't have to select each individual message individually. For example, Gmail lets you search for specific keywords or email addresses in your email and then select them all to quickly move many emails into a separate folder.