How to edit "home" page

Hello,

I have a problem that has been discussed here many times – editing of a “home” page (or front page).
I need a solution that could work for my case: http://www.stopp-schnarchen.de
I work with wpml and managed to translate my German “Startseite” into “Home”. Because I need to make other changes on both sites I need to access them again, but they are not shown in the list of pages anymore.

How can I proceed? I read about two ways of doing it:
1. Create new “Home” page and overwrite this way the old one or
2. Access and edit home.php, what seems kind of complex for me since I would need to add slides to the page that I’m editing.

I would appreciate your advice and also any links to comprehensive documentation.

Thank you

wzag