I'm new to programming in general, and I'm currently working on a little game project in Python + pygame. One day I might want to work on my laptop, and the other day on my desktop. How could I make it so that I can continue on my code from whatever computer I'll be working on? You could compare it to working in the same document in Google Drive, from whatever device you want. I've seen services like Github, Google Cloud Code, Microsoft Azure... could they be what I'm looking for? Would it work storing my project folder in something like Microsoft Onedrive?
Onedrive could work, but I would suggest that you take a look at Git or any other version control system. As you progress with your development as a programmer, you most likely will need to use some kind of version control system when working with code (hopefully as a profession).
And yes, git and some web-based repository hosting service (github,bitbucket,gitlab... to name a few, and there are lots more available) will allow you to work on any number of computers and keep your code "up to date" on all of them.
So look into git and learn a new tool at the same time.
Welcome to StackExchange !
As a long-time developer, I highly recommend you to learn git.
It will make you able to work from anywhere (Github even has an editor on its website). But most importantly, it will allow you to easily share your code and have multiple people working on the same project without (too many) headaches.
This really is the standard in development nowadays. It is a skill that will stay helpful for a long time.
As mentioned you should learn git and use a service like github, but Microsoft have recently launched a service called CodeSpaces which is pretty cool and will also solve what you are after.