How can I repair partition map after attempting to dual boot screwed it up?
If your Mac's a Late 2011 or later model you should be able to use Internet Recovery - Apple support page here. You could always install OS X on an external USB/Firewire/Thunderbolt drive which would then give you option of retrieving whatever you need from your internal drive before thoroughly wiping it clean. Personally I like Fedora Linux for this purpose, boot up from USB and go into the Disks utility where you will quickly be able to delete all existing partitions including the hidden EFI section, guaranteeing a clean slate before setting it all up again.

If it's an earlier model then you'll need to find someone with the installer for 10.7/8/9/10 and make a USB installer from it, or find a late retail copy of Snow Leopard (the last copies had 10.6.3 which will start up any Intel Mac before 2011).