While we cannot talk with any authority about the wider issues of freedom, we can and will encourage you to spread the gift of Software Freedom in this festive period. There are, of course, many free operating systems available to you, including the various Linux distributions, BSDs, etc. However since we're a mostly Linux-focussed website, we'll only look at Linux.
Now, as you're all undoubtedly aware by now, I am very heavily biased in favour of Debian as an operating system. But if you are going to be gifting software freedom to someone soon, it may make sense to use one of the Linux distributions more geared to less familiar-with-UNIX users.
There are a number of supposedly better-for-beginners distributions, but an article about linux distributions for new users suggests Linux Mint, Ubuntu, and Linux Deepin. Within the Ubuntu fold there are a number of options, but if I were to go Ubuntu I'd probably go XUbuntu for a beginner.
Whichever option you go for, most distributions provide live "CD"s with installers built into them. This allows the recipient of your gift to try it out before installing it onto their system. Just in case they're not quite ready for all the power, flexibility and freedom that such a gift brings them.
Once you have a copy of the live image on your computer, it's time to get it written to some medium you can supply to your unsuspecting receiver of the joy known only to those with liberated computing experiences. There are various options -- obviously as mentioned above, these are often referred to as "CD" images, although rarely these days do they actually fit on a CD. More often than not, they're DVD-sized, but a DVD writer is a pretty common piece of equipment. If you lack that, or they lack a DVD drive in their computer, you may be better off finding a USB stick (I suggest buying a nice one, after all packaging up the gift is part of the fun) and install it on that.
Whatever distribution you choose, or even if you choose a BSD, or simply to help someone install some free software on their non-free platform (e.g. installing GIMP on their Windows box.) don't forget that the most valuable thing you can gift alongside the installer is your time to encourage, assist, troubleshoot and ultimately free your friend/family-member/random-stranger/lover.