I have Windows 7 installed, and it's taking up 51GB of space. I don't know whether or not it is in a partition in my C drive, but I have 450GB free space.
When I install Ubuntu does it use ALL of the free space as a partition for Ubuntu, or does it just use whatever amount it needs? I'm hoping the installer will know how much space to allocate to Ubuntu and not take all the free space.
First, The C drive in your Windows 7 is a partition and most likely a primary partition. Your computer may have other partitions, such as the recovery or the systems partition. A computer can have up to 4 primary partitions. If yours came with 4 already, you won't be able create new ones needed for Ubuntu installation without deleting one primary partition. The newer computers with GPT partition table does not have this limitation. Let's say for now, your computer does not have this problem. You should read more about disk partitioning to familiarize yourself with various terms.
Second, During the installation of Ubuntu from a Live CD or USB you will get three choices:
Install side by side with Windows
Replace Windows 7
Something Else
The third choice are for advanced users. The first and second are self explanatory. I think you may want to stick to the first. Read the answers to this question for an overall description: How do I install Ubuntu?.
Third, when you choose the first option you will be able to decide how much space you want to allocate to Ubuntu and how much to retain for Windows. See this questions for some explanations on this choice: Installing Ubuntu with Windows, which is left and right when allocating space?.
When you make that choice, the installer will use the space you allocated and create the two necessary partitions needed for Ubuntu, the / (in ext4 format) and the Linux Swap.
As for how much space you should allocate, that is a different question.
I hope this is helpful.
