I own a MacBook Pro running Mountain Lion. I would like to dual-boot my Mac OS with Ubuntu. When I download the file and try to open it, it reads "No mountable file systems". I have downloaded both the 64 and 32 bit software. Can someone help me through this process?
You need to set up the Mac so that there is a valid file system for Ubiquity to find and start installing to. Have a look at the Mac installation wiki and go from there as they have done a wonderful job already.
Has to be an EFI boot, I installed x64 Ubuntu on my schools mac last year in highschool along side to the mac os, im pretty sure all i did was download the ISO and used Disk utility to put it on the flash drive, you can use Rufus https://github.com/pbatard/rufus/wiki/FAQ Fat32 EFI partition, good luck!
You do not need to use Refit or any other boot manager / loader since as far I know these emulate BIOS when Ubuntu can boot no problem at all using EFI (I may be talking a load of rubbish here since I don't particularly know all of the technical details).
In short you don't need Refit!
To get started head over to the Ubuntu community Wiki here and find out what model your Macbook is (in OS X you can do this by clicking on the Apple logo in the menu bar and going to "About this Mac" --> "More Info" --> "System Report" and then look for the "Model Identifier").
Follow the relevant guide (for my late 2013 Macbook Pro I used this guide https://help.ubuntu.com/community/MacBookPro11-1/Trusty).
Sleep mode may or may not work (for me it doesn't and I have no idea how to fix it)
The iSight camera doesn't work (again with a bit of research I may be able to fix this but have no idea how to)
You may not be able to power off or reboot properly (I had to alter the grub config file in order to fix this but do not remember the alterations I had to make)
Best of luck to you and hopefully you'll figure everything out!