Although you can still do this in the New Google Drive, the keystoke has changed to the nonsensical “Shift+Z” to open up the “add to” dialog. Thank goodness you can still hold down control (or Option on a mac) while you drag things from one folder to another in drive so you don’t mess with the permissions while you are adding it to your own folder structure. I know they are trying to simplify things, but I don’t think this is the right way of going about it.
Advanced users can add the file to ‘My Drive’ instead of moving it. This is not a copy of the file. It’s literally the same file located in multiple folders. For example, renaming the file in My Drive will rename it for everyone and sharing it will share the original file with anyone the added file is shared with. Users can do this by selecting a file and then pressing Shift+Z to display the “Add To” dialog box.