Unfortunately, you'll get a lot of completely unhelpful information on the Internet about this, since the boot process on UEFI-based systems is completely different from the boot process on older BIOS-based hardware. Completely describing the relevant differences in one post here is impossible, so for full information, I recommend you check out the Wikipedia page on UEFI and my Web page on EFI boot loaders for Linux. (Note that "UEFI" refers to the next generation of EFI; essentially EFI 2.x. For the most part, the two terms are interchangeable, although "UEFI" is more specific and refers to a newer version of the technology.)
To get you started, though, you should first verify that you are booting Windows in EFI mode. This can be done in a number of ways, such as typing "bcdedit" in an Administrative Command Prompt window. The result should include a reference to winload.efi in the "path" line of the "Windows Boot Loader" section. If instead this line refers to winload.exe, then the system is booted in BIOS mode, and you need to follow more conventional BIOS advice for this.
Assuming you're booted in EFI mode, my first advice is to forget about installing Ubuntu 11.10 or earlier. These versions include bugs in the installation process that make it much harder to set up a dual-boot with any other OS. Ubuntu 12.04 fixes the worst of these bugs. In 12.04 booted in EFI mode, the installer should detect the EFI System Partition (ESP; a partition that holds boot loaders) created by Windows and add its own boot loader to that partition.
One possible complication is that Ubuntu might not boot in EFI mode, even if Windows is installed in that mode. You can check this detail by looking for the directory /sys/firmware/efi. (You may need to use the "try before installing" option to check for this file, then launch the installer.) If This file is present, you're definitely booted in EFI mode. If not, you're probably booted in BIOS mode, although that's not 100% certain. If you find you're booting in BIOS mode, you should either correct that problem or go ahead and install in BIOS mode and switch your boot mode afterward. Either of those options is worth a whole new question here, so I won't go into them.
Ideally, if Ubuntu 12.04 installs correctly, it'll detect Windows and make GRUB 2 the default boot loader, so the system will work as expected, offering you a boot menu when you boot. Sometimes, though, you'll need to add Windows to the GRUB configuration, which you can do by creating an entry like this in /etc/grub.d/40_custom and then re-running "grub-mkconfig -o /boot/grub/grub.cfg":
menuentry "Windows 7" {
set root='(hd0,gpt1)'
chainloader /EFI/microsoft/BOOT/bootmgfw.efi
}
Other times the system may continue to boot straight into Windows. This can usually be corrected by deleting EFI/boot/bootx64.efi from the ESP, or perhaps replacing it with a copy of the GRUB 2 boot loader file (probably EFI/ubuntu/grub_x64.efi, IIRC). Unfortunately, this problem is caused by bugs in specific EFI implementations, so the workaround can be highly system-specific.
Your symptom of a black screen with a blinking cursor suggests a serious GRUB misconfiguration, or perhaps a completely missing GRUB installation. I'm going to duck this question by saying that with any luck it will be fixed by Ubuntu 12.04. If not, I recommend installing ELILO or Fedora's patched GRUB Legacy to replace GRUB 2, since in my experience GRUB 2 is the least reliable of the available Linux EFI boot loaders. (See the EFI boot loaders page I referenced in the first paragraph of this reply for details.)
