Linux is a term commonly used to describe the collection of operating systems running on the Linux kernel. Examples include Debian, Ubuntu, Linux Mint, Red Hat, Fedora, Open SUSE, Arch Linux, Kubuntu and so on. This collection is arguably the most diverse ecosystem of operating systems on the planet.
Just about every computer can run one form of Linux or another, though typical minimum specs are a 1 GHz single core processor with 512MB RAM, and around 5GB of hard disk space, and faster machines are recommended, though some flavours of Linux are considerably smaller, at around 512MB total for the disk space).
Reasons for using Linux
If you don't have the funds (which may be the case as a student) to replace your older hardware, but that hardware isn't fast enough to run any version of windows past XP (which is almost a decade old), or you have a netbook with limited system resources, then getting a faster OS for free to do your word processing and other options could be a good move, and improve your productivity and continue your support for updates forever. In addition, Linux is less of a target for malware as it is less commonly used compared to Windows and Mac Operating Systems. However, some malware for Linux does exist but there are plenty of free security packages available.
Software compatibility with Windows
This is the greatest problem people face in Linux. While you can get most programs to run fairly easily in Linux using WINE there are some programs which are incompatible. An example would be Microsoft's Internet Explorer, but there are open source replacements for all programs on the system, though games will require a native Windows OS. Then again, Linux programs don't run on Windows. For games you will have to install WINE (A program compatibility layer for windows that runs on Linux and Mac) and check WineHQ appdb to see if it can run your game and what may not work in the game on Linux. Anything regarded as below gold is not guaranteed to run smoothly, so, if you have room, keep the old Windows as a partition if it is likely that you want to play a game that won't run under WINE.
http://www.osalt.com/ is a free software directory that can give you many open source alternatives to popular windows programs that may/may not work through WINE.
Most Linux operating systems are available to download at their websites (linked below) in an ISO file. an ISO file is basically a file containing lots of data to be burned to a disk using a tool such as IMGBurn for Windows, or using a disk burning tool in the Mac OS. Netbooks can use UNetBootIn to transfer it to a USB stick to use).
After that's done, keep the CD in the drive, and change your BIOS settings to change the boot order so that the CD drive boots first (press the button that says to go to the boot device selection menu when the BIOS loads), and a menu should pop up, prompting to try the operating system out, or install directly. Feel free to try the system out, to check if the hardware works, or if you like the look of the operating system. If it feels a little sluggish, that's because the CD drive is slower than the main disk, the OS will be faster once installed. Once you're ready, there should be an icon to allow an install. From there, it should be an easy process.
An install guide for Linux Mint is curently available here but will be updated.
Install guides for Ubuntu, Fedora, Debian, and OpenSUSE will be available when their individual articles are written.
Links to websites for distributions
Ubuntu (based on Debian)
Linux Mint (based on Ubuntu)
Fedora (Based on Red Hat, has become home OS for Red Hat Linux)