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Do you want to try with the idea of a future install or just by curiousity? Wanted to give you a more complete answer.
1. Live CD.
If you want to try an OS like Linux, many comes with an option called live CD (you download an ISO image, burn it into a CD/DVD and you can boot with it to test it without the need to install it). It is slower than a full install but it will give you an idea of some of the technical problems like drivers that you might encounter when/if you decide to install it.
2. External disk
This is what I usually do, I installed the OS on an external disk or usb pen, so I can boot from an external disk and completely enjoyed the OS at nearly full speed. I have a laptop and I boot from an external harddisk for personal stuff on Ubuntu and the internal hd has Windows 7 for Business purpose. (for the install on an external HD on a laptop, I usually remove the internal HD when I do the install on the external hard drive in order to avoid overwritting by accident the internal hd. I have done it, so I learned this easy trick).
3. Virtual machine
You can use VMware or Virtual box. It is good to try but it is not the best way to have an idea of speed and potential driver problem. This is best if you machine has enough CPU and memory as the resource will be share between the two OS...
4. Second partition or second harddrive
A lot of the Unix versions offer the option of freeing some disk space to install the new OS without removing the current OS. For instance Ubuntu, will detect Windows and propose to reorganize the disk to create a new partition for Ubuntu without overwritting Windows but it will modify the boot sectors to create a dual boot menu to choose to boot on WIndows or Ubuntu in this case.
5. Buy a cheap computer
You can buy a cheap computer on ebay or refurbished to try the new OS...
There are a couple of ways to do this but it sounds like you would be best off using a virtual environment like VirtualBox to run these inside Windows. You’ll need the ISO images for both Ubuntu and Mint (donate, if you’re able) to burn to a disc or ideally, run in a virtual disk drive (saves you a disc - the “green” option :D ) Use DAEMON Tools Lite (the free version) to create virtual disc drives that behave just like a disc drive without the need for an actual disc.
After you have acquired the ISO files and other software, open DAEMON tools and both a DT and SCSI drive, in case one doesn’t work, by clicking the button below the Images pane. After the virtual drive is created, right click on one of icons and select the Mount option.
When you’ve completed the above steps, open VirtualBox and click the New icon. You’ll go through a wizard where you select the parameters of the OS you’re installing. After everything is appropriately configured, you’ll click on the icon for the OS you created in the VirtualBox console. From here, it’s just like installing an OS on a normal machine. Fortunately, if none of this makes sense, there’s little chance you’ll destroy your machine, so have fun!