Well, I'm glad you asked. Like most of the Chromebook services, it starts with Chrome. First thing you must do to access your home / office machine is to install chrome on it. Once you get chrome installed, then it is as simple as adding Chrome Remote Desktop to your home machine. This will allow you to open your home / office machine to be "remote controlled" by your Chromebook. This will have the effect of making your Chromebook a remote keyboard / monitor / mouse (KVM) to your home PC.
Now.. the the technical stuff behind that isn't all that amazing. The "remoting" opens up a pipe (of sorts) between your Chromebook and your PC / Mac. Once that pipe is open, you can open any files that you might have at home as if you were sitting there. If, on the other hand, you want to pull some files off of your home machine, the answer is equally simple. Just push them to the "Google Drive" or some other shared google service that both your home PC and your Chromebook can access. Once you kick the tires on the process, the whole thing is not as hard as it may sound.
I'll spare you the gory details of how to do this, but if you want a step by step guide, check out this nice How-To Geek write-up on it. I just wanted to give a quick post out to let you know it can (easily) be done.
Like anything tech... I'd shake out the process a little bit. If at first you don't succeed, just start rebooting and retrying in hopes of something falling into line. It worked as expected for the most part, and the bumps I hit were for genuinely unique configs that I run. The good news is once it works once, it generally works forever.
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