With a new SharePoint version, come also new MasterPages, with differences in both technology and design considerations (HTML5, CSS classes...). So, to get started with creating your 2013 targeted branding solution, you can either copy Oslo or Seattle and start with those, or do the (in my opinion) slightly easier approach and download the 2013 Starter Masters by Randy Drisgill and use those (read the instruction on the page before using).
One cool thing about the 2013 MasterPages is that the same MasterPage applies to search sites too so you don't need to be creating a separate one for that anymore.
Location of design files
Note the url to the files in the MasterPages Gallery (with the exception of the icon and tile image files, that need be referred to with a simple url /_catalogs/masterpage/mydesignfiles/favicon.ico):
You can also use the mapped Layouts folder like before, but the reference path to the virtual directory has changed; instead of the simple
you need to insert '15' in the path (note: do not manually add it in the mapped folder structure in VisualStudio, only in the reference path):
As stated in my earlier post(s), you can create separate MasterPages to be used with different devices and add device channel panels to Page Layouts to target content to specified devices. Even though it might be called for in some occations and a good practice in many, I would recommend to at least consider responsive design of your MasterPages and Page Layouts instead. It is not only easier to implement (no need for manual setup), but also more efficient in the wolrd of a million plus one different devices, when instead of differentiationg between OSs or browsers, the pages adapt to different resolutions fluently.