I have some experience with JavaScript but none whatsoever with JavaScript project management and tooling. I'm looking at using node and AMD but am not exactly sure what they are used for and am having trouble wading through the documentation.
Here are some of the specific points I'm stuck on:
These projects aren't related.
node.js is a JavaScript interpreter just like a web browser. It's a server technology and can't run on a client. Specifically it is a wrapper set of libraries that add IO support, to file or network, so that you can read from disk or respond to TCP (and therefore TCP/IP aka HTTP(S) or FTP) requests. Otherwise, it's just javascript like you would write in the browser. You can use it to run script from the command line or build a web server.
It can be used to "build" projects from the command line since it's able to be used like a scripting language in a shell environment (it even responds to #! command routing).
AMD is a tool to manage dependencies for JavaScript projects. You can use it load dependencies dynamically and even asynchronously (hence the name). AMD will work in the browser and in node.js (but node.js already includes a technology to load JavaScript dynamically, so it won't be really useful).