How do I add new pages such as an 'about' page or my own 'news' page?

Depends on the theme used. If it supports the Zenpage CMS plugin, just turn it on. Otherwise you have to extend the theme following our theming tutorial.

I'm using the zpGalleriffic theme. I have added my own pages (about, gear, etc) via the 'pages' admin, but when I try adding my own homepage, two such 'home' pages appear in the header menu, one of which links to the 'gallery' page. How can I get this theme index.php (or wherever) to link to my own custom homepage instead of the current album 'gallery' page?

As a rule, always add the name of a third party tool to the topic so its author can help (the text below the form does tell that btw). I have no idea how this theme creates its menu or if it supports the Zenpage homepage feature.

I have seen other websites which use the zpGalleriffic theme and they somehow seem to be able to customise the header menu to suit their own individual requirements, so obviously it can be done. I will persevere until I find a solution but thanks anyway acrylian.

I took at very quick look and it seems the home page (index) is hardcoded in the inc-header file.

In themes options you can add a home page.
you have to create a page which stays unpublished and then you have to chose this unpublished page as home page in the relevant option.

btw, when you are logged, this page appears twice : one as your home page, one as a page. your visitors can see only one (home page)

Thanks vincent3569, followed your instructions, now works a treat.