You set up the styles with the setting of "Style for following paragraph" set to do this. I.e., in heading 1 style you have it set for the following style to be heading 2 rather than normal. I have my heading 1 set to be followed by heading 2, and my heading 2 set to be followed by heading 3.

This is done in the modify style dialog.

Note also that if you are using the built-in heading styles, there are built-in keyboard shortcuts for Heading 1-Heading 3. Ctrl+Alt+1 = Heading 1
For more shortcuts, see Heading Style Keyboard Shortcuts Add-In for Headings 4-9.