So I'm still a Linux beginner. I'm looking at buying this hp pavilion for work: http://www.pcworld.com/product/1264284/hp-pavilion-10-e010nr-touchsmart-notebook-pc.html
I'd like to have Linux on it to fool around with, but I want all the HDD space for work and win8. Can I put a distro on an external drive? I've read that Linux doesn't distinguish between separate drives, only separate partitions. How much truth is there in that? Will that be a problem? I've never had multiple drives hooked to any of my other linux machines and I don't currently have a machine to try this on before buying.
Install a distro on to a usb stick. 16 or 32gb sticks are cheap enough these days.
Yeah you can run a live distro like Linux Mint off a USB drive, use unetbootin to set it up, but it won't be persistent by default. You'll be able to get online and use the default programs (like firefox) and install programs but once you turn it off the new programs you installed disappear. Making a full persistent install on a USB stick will require a little google fu but it can be done. The other tricky parts will be disabling secure boot (it's a setting from within windows not a hack) and getting into the bios/uefi settings to set to boot to usb. Getting into the bios/uefi settings is tricky because uefi systems boot to windows without giving the "the press whatever key to enter settings" message, you'll have to google your system to find out what key it uses. You may also have to "enable legacy OS support" from within the uefi to boot anything besides win8.
I won't go all Tl:dr with my philosophy but you will probably have more headaches using a live install long term than you would from investing 10 or 20 gigs in some dual booted linux goodness.
Continuing with Jethro's thought, I would recommend siphoning a little bit off for Linux (of a 128GB SSD, I had ~90 for Windows and ~30 for Linux, though you probably won't need that much), and then using your external hard drive as, say, your /home partition. There's only one problem - the hard drive will have to be formatted ext4, as opposed to the ntfs partitions that Windows embraces so much. That means you won't be able to see any of it in Windows - but if you were planning on partitioning a reasonable amount of space for Linux in the hard drive, I'm sure you could figure it out.
You *could* just run a liveusb, but then you wouldn't be able to save anything across sessions, from applications to whatever files you created. You can't really install Linux on an external drive explicitly, because you need an OS to be able to access an external drive.
Your third option is virtualization (using a virtual machine). This is probably the safest option as far as keeping all your data safe and keeping your Linux sessions, but it could also be more complicated in setup. I won't elaborate on this much since I don't have much experience with this, but there are plenty of other people that could help.
Oh, and as for the drives thing, that's pretty much false. Yes, it sees partitions, but it segregates them by disk. On any reasonable distro, it will be able to see whatever drives and partitions you have, and even whatever operating systems you have installed on them. Most any distro will give you a lot of flexibility with where your Linux partitions end up.
Yes you can install it on an external drive without problem.