Question: We've got an Asus X501A laptop (dec 2012) which has this UEFI thing. If I boot from an USB it only offers me to wipe the entire hard disc and install the new distro, or manual partitioning which I can't get my head around due to this UEFI thing.
-- Note that this question has nothing to do with that other operating system named after openings in walls. Not interested in that.

Answer: 
When you reinstalled Windows, it took over your MBR with it's own boot loader. Your Ubuntu is still fine you just need to restore GRUB so you can dual boot. You want to use [a tool called `boot-repair`](https://help.ubuntu.com/community/RecoveringUbuntuAfterInstallingWindows).

EDIT:

With no optical drive, your best bet is to boot a live distro via USB. For this, [download an Ubuntu iso](http://www.ubuntu.com/download/desktop) and then [flash it to the USB as a bootable image using Unetbootin](http://unetbootin.sourceforge.net/). This is my preference when rescuing systems using a "live CD." It allows you to get the same effect using a disc or requiring an optical drive.
If you can boot from USB, your answer is [there](http://www.ubuntu.com/download/desktop/create-a-usb-stick-on-windows)

If your machine has room for more than one HD, and you can borrow one for some time, you can set up the temp HD as primary, install Ubuntu on it and fix the [MBR](http://en.wikipedia.org/wiki/Master_boot_record) from there. Hello screwdriver, hello headheache, but in the end it will be fine.