Hi I was wondering how to back up my computer OS and my stuff before formating the hard drive and instaling Ubuntu because I do not want to lose my stuff and my OS. Also I do not want to buy a new hard drive
You should back up your hard drive before you install Ubuntu just like you back up your hard drive all the other times you regularly back up your hard drive. If you don't regularly back up, this is a great time to start, whether you continue and install Ubuntu or not. To do this, you need a second hard drive, because you need someplace to copy your files to, someplace off your computer's hard drive for the copies to sit, safe from any disaster that might befall your computer or its hard drive. There is really no other way, short of subscribing to a cloud backup service.
Assuming you're going on to install Ubuntu and keep your current OS (Windows? I can't tell because you talk of saving your OS and formatting your hard drive. You wouldn't want to do both.), you should find a Windows backup solution that works for you. There are lots of programs available to make a copy of your entire hard disk or parts of it to a USB drive. You have to have the USB drive. Buying anything smaller than 2TB is a waste.
Your next problem, assuming you want to save your current OS and install Ubuntu is deciding if you're up to creating a separate partition for your user data so it can be available to you when you boot to your old OS or your new Ubuntu OS. You'll need to look up "ubuntu dual boot" on Google and research your options and see what fits your needs and your skills.
i say you should use crashplan so that you can move your files then to linux but the only issue with crashplan is that its a little complex to setup
here it is: http://www.crashplan.com/consumer/crashplan.html
(its a full version if you use it with local and friend computers so dont worry its no virus, if your unsure i made a virus scan here: https://www.virustotal.com/ca/file/5fde5ce803958764f09e21e9bc7a0404a8cfe7dfe74c9d7f374f239d291b4e92/analysis/ (virus total scan))