Alright, time to pass out directions.
I've been running a UEFI Win8/Ubuntu dual-boot for about 6 months now. It's not a problem to do as long as you understand UEFI's quirks.
To start with, you'll need to partition your hard drive. This can be done through Disk Management in Windows8. You'll need to SHRINK your C: drive by the approximate amount of space you wish to let Ubuntu have, and you'll need to let it stay as "unallocated space". Do not format the space after shrinking it! If you need help to do this right, let us know. Do not try to do it with out having us walk you through it if you aren't already familiar with drive partitioning. You could lose your data if something goes wrong.
Now, head into the BIOS. Somewhere (probably under boot devices or boot options) they'll be a setting for Secure Boot and possibly Legacy Mode or Compatibility Mode. You want to DISABLE BOTH. This will both turn off Secure Boot AND filter out any non-UEFI boot devices available.
Next, head to Ubuntu.com
and download the 64-bit, UEFI-aware version of Ubuntu 13.04
, burn it to CD (or use LiLi USB Creator
to put it on a USB device), and reboot your machine.
Hit F9 (or whatever Key Gateway Machine's use to select boot device, on HPs it's been F9), and select your boot device you're gonna install from. It must say UEFI somewhere in the device entry. There's a big difference in launching from "Internal CD/DVD ROM Drive" and "Internal CD/DVD ROM Drive (UEFI)!
Once you've launched the Installer in UEFI mode, follow the directions and select "Install Ubuntu alongside Windows 8". Let the installer do its thing.
Now, here's where everyone's problems with Win8 and UEFI and alternate installs come from. It'll ask you to reboot. Do so. If you don't hit any keys as the system starts up, it'll go directly into Win8, with no sign of GRUB anywhere. This is because the UEFI system is set to OS Boot Manager as its default boot device, and THAT has tunnel vision only for Windows installs.
How to we stop this? Simple, really. In the current setup, every time you want to go into Ubuntu, hit the F9 key (or whatever you used to get that menu where you selected to boot off the install disc) during bootup, and the list of boot devices shows up. In this list is now an entry to Ubuntu. Select it, and you'll be sent off to grub and so forth.
A little annoying, yes, but stable, and works as advertised.