Steps:

SiteActions (gear icon) > Edit page
From Ribbon: Insert > WebPart
Category: Media and content > ScriptEditor
From webpart: Edit WebPart -> 'edit fragment' appears
Edit Fragment: opens dialog box; insert all-in-one code, below
Click 'Insert'

All-in-one:

<style type="text/css">
#sideNavBox { display: none }
#contentBox { margin-left: 25px }
#titleAreaBox #SearchBox {display: none !important;}
#DeltaPlaceHolderPageTitleInTitleArea {display: none !important;}
#suiteBar {display: none !important;}
#s4-ribbonrow {display: none !important;}
</style>

<style type="text/css">
<!-- hide quick launch left menu -->
#sideNavBox { display: none }
<!-- move page content to the left side of the page, in the space where the sideNavBox was -->
#contentBox { margin-left: 25px }
<!-- hide search box (nestled within the titleAreaBox) -->
#titleAreaBox #SearchBox {display: none !important;}
<!-- hide pagetitle (useful when using a url that differs from the pagetitle) -->
#DeltaPlaceHolderPageTitleInTitleArea {display: none !important;}
<!-- hide topbar (SharePoint, Newsfeed, OneDrive, Sites, [username], settings-cog, help) -->
#suiteBar {display: none !important;}
<!-- hide 2nd topbar (browse, item/page/library, share, follow, sync, edit, fullscreen) -->
#s4-ribbonrow {display: none !important;}
</style>

When committing these changes, the last item in the list (s4-ribbonrow) will hide your 'edit' button. In order to be able to edit the page once it's hidden, append the following url-part after the url of the page:

?ToolPaneView=2&pagemode=edit

This will allow you to edit the scripteditor webpart, temporarily remove the lines that hide the ribbon, and thus give you back your 'edit' link. Make sure when you're done to save the page before adding these lines back in the webpart.