I recently got this Toshiba C75D-B7300 and I want to mess around with it and I've come across ubuntu which I think is a great OS about getting out of windows 10 (upgraded from windows 8.1).
But before I do anything I just want to ask: if I install Ubuntu, will any of my drivers work or will I have any problems?
Ubuntu has open-source drivers for almost everything. Everything should work out of the box.
Although, take note that you may have some issues.
It is not too uncommon to have issues with Wi-Fi, and your life is practically over if you have Nvidia Optimus. (The optimus part doesn't apply to you I think, since at least from what I could find you have integrated AMD graphics)
I wasn't able to do any research on the Wi-Fi, since the official "spec sheet" is EXTREMELY vague.
Just burn the 16.04 ISO to a blank DVD, and try it in live mode to check if everything works.
I recommend burning to a DVD ^^^ rather than onto a USB drive since for some reason new users always have problems successfully burning a USB stick.
If you don't have a blank DVD, and want to try a USB stick, I recommend this program, because it has the highest success rate: http://www.pendrivelinux.com/universal-usb-installer-easy-as-1-2-3/
While Android Dev made a great answer, I want to add a few things.
First, I'm going to start out with a bit of a tip. We're here to answer your questions, but we generally don't like having to research your computer to get its specs. People have different variations of the same model, or even custom models, and it can be tricky trying to figure out how to help when there are, say, 5 different possible network cards. With that said, I do appreciate you at least giving the model of the laptop. There are many people who come here to ask who don't give any specifics at all.
Now for an answer.
Even with your model number, I had trouble finding very detailed specs online (even though the PDF I opened from Toshiba said "Detailed Specs"). However, I was able to see that your computer has AMD graphics. With the release of Ubuntu 16.04, AMD cards no longer have proprietary drivers available. The end result of that is usually a huge lack of performance.
If you need to game or watch a lot of videos, I suggest you install Ubuntu 14.04 instead of 16.04. 14.04 still has drivers for AMD cards that will give you good performance. You cannot install fglrx (the AMD proprietary driver) on Ubuntu 16.04. It will break your installation.
Since I couldn't find any other specs on your model, I have to assume and say everything should work. You should only worry if your Wi-Fi card is a certain Broadcom series or a Realtek. Both have relatively easy fixes, but they are a hassle to set up.
Other than graphics and network, you shouldn't have to worry.
