I am trying to get my node environment set up on a new Ubuntu 12.04 instance, with Node 0.8.14 already installed, but I ran into problems when I try to run npm install
OP here, I have learned a lot more about node since I first asked this question. Though Dmitry's answer was very helpful, what ultimately did it for me is to install node with the correct permissions.
I highly recommend not installing node using any package managers, but rather to compile it yourself so that it resides in a local directory with normal permissions.
This article provides a very clear step-by-step instruction of how to do so:
https://www.digitalocean.com/community/tutorials/how-to-install-an-upstream-version-of-node-js-on-ubuntu-12-04