The Raspberry Jam Mod, for Forge and Minecraft 1.8-1.11.2 (1.9-1.11.2 is recommended), implements most of the Raspberry Pi Minecraft protocol.
The protocol lets you run python scripts to draw stuff in Minecraft. A nice introduction is here.
The scripts I've tested run without modification on my Windows system with the mod. Of course, you need python (or go or Haskell, all of which have libraries for the protocol, I believe).
Previously, doing this required either buying or emulating a Raspberry Pi, or setting up a Bukkit server with the Raspberry Juice plugin. But for playing around in single-player, running your own server is overkill.
I am completely new to Minecraft modding, and indeed know almost nothing about Minecraft. Writing this mod over the last two days was literally the most time I've ever spent with Minecraft. I probably screwed up in multiple ways. I did this for my daughter, to encourage her learning python. [Edit: Well, this was true when I first released the mod in 2015. Now the mod has gone through many, many revisions.]
I have now implemented all of the Raspberry Juice protocol for singleplayer, and added a /python script command that lets you run script.py directly from Minecraft. Just unzip all the contents of mcpipy-master (including subdirectories) in mcpipy.zip into a mcpipy subdirectory of your Minecraft directory (the same directory with your mods folder) and you can then, e.g., do /python nt7s_sphere to run the sphere script.
I've also run across another project that implements the Raspberry Juice protocol in a mod for 1.7.10. I got the idea for the /python command from them.
You can get and install overwolf which is a free application that will both allow you to live stream and make videos, as well as a bazillion extra abilities.
Or you can get bandicam from http://www.bandicam.com and use their free version to make 10 minute vidoes that posess a watermark. I use bandicam for my videos as feel it is the best. I've tried fraps and others but felt them to complicated to use or cumbersome.
From there it is a simple matter of uploading the video.
Alternatively, youtube offers its own tools for recording the screen and uploading as well as streaming, but I don't think their streaming is all that popular.
I've just released 0.14. I've made some bug fixes. And I've updated the instructions in the Instructable.
The latest version of my python scripts package also enhances the turtle graphics package with code for drawing filled polygons (startface() and endface()) and a push()/pop() state stack which makes it possible to implement L-systems. For instance the following tree is drawn with turtle graphics driven by an L-system based on geeky.blogger's rules (with parameter changes): lsystem.py in my package.
After running the installer, you can edit scripts with IDLE for Minecraft Python (link on desktop and in start menu): File|Open and then you can see lots of samples. You can also run scripts right from Minecraft. Some fun things to try: