Do not disable UEFI if you plan on dual-booting. The general rule is either both UEFI or both MBR, but mixing does not work (one OS will not be visible and won't boot).

Then, install Ubuntu on a separate partition (see other guides for that).

Now, Ubuntu will have installed GRUB2 as the UEFI bootloader, and you will be able to start Windows from GRUB2 (Ubuntu adds the "Boot into Windows" option automatically). At this point, most people are done. Booting will be UEFI->GRUB2->Linux or UEFI->GRUB2->WindowsBootMgr->Windows, thus you will be chainloading Windows through GRUB2.

If you'd rather have two different UEFI bootloaders so that you can select Ubuntu or Windows directly from the BIOS (like you would select booting from the DVD drive etc), you can follow the guide here or my abridged version on SuperUser here.

Then, booting would be UEFI->GRUB2->Linux or UEFI->WindowsBootMgr->Windows, and there would be no chainloading.

If you plan on doing this, I recommend you make a full backup of your /EFI partition and the files on it from Windows before proceeding. Mounting the EFI partition is described here or on SuperUser here.

EDIT, to clarify on whether you should install using UEFI or not: What is set in your BIOS is not that important. What is important is whether your Windows was installed using UEFI or not. If it is, you need to install Ubuntu using UEFI (the liveUSB needs to boot using UEFI). If Windows does not use UEFI, then neither should Ubuntu.

See also here: https://help.ubuntu.com/community/UEFI#Case_when_Ubuntu_must_be_installed_in_EFI_mode

Checking whether your Windows is booted as UEFI: Multiple possibilities are described here

Checking whether your Ubuntu (Live CD) booted as UEFI: Multiple possibilities are described here