Enabling two entirely separate menus

I’ve already had a very helpful response to a problem I encountered using WordPress as a CMS, so I’m hoping someone can point me to a solution for my other difficulty. The context is that I’m an experienced (X)HTML/CSS developer with zero knowledge of PHP and WordPress, who as a favour is setting up a series of small sites for highly un-techy users.

I’m trying to replicate a basic design pattern: a top-level horizontal menu as in Twenty Ten’s default, and an entirely separate secondary menu in the sidebar. I also want users to be able to switch between menus for link management.

I’ve read the Custom Menu documentation but I’m unclear what combination of plugins, widgets etc would work, if any.