Node.js Question:

First, learn the core concepts of Node.js:

You'll want to understand the asynchronous coding style that Node encourages.

Async != concurrent. Understand Node's event loop!

Node uses CommonJS-style require() for code loading; it's probably a bit different from what you're used to.

Familiarize yourself with Node's standard library.

Then, you're going to want to see what the community has to offer:

The gold standard for Node package management is NPM.

It is a command line tool for managing your project's dependencies.

Make sure you understand how Node and NPM interact with your project via the node_modules folder and package.json.

NPM is also a registry of pretty much every Node package out there

Finally, you're going to want to know what some of the more popular packages are for various tasks:

Useful Tools for Every Project:

Underscore contains just about every core utility method you want.
CoffeeScript makes JavaScript considerably more bearable, while also keeping you out of trouble!
Caveat: A large portion of the community frowns upon it. If you are writing a library, you should consider regular JavaScript, to benefit from wider collaboration.

Unit Testing:

Mocha is a popular test framework.
Vows is a fantastic take on asynchronous testing, albeit somewhat stale.
Expresso is a more traditional unit testing framework.
node-unit is another relatively traditional unit testing framework.

Web Frameworks:

Express is by far the most popular framework.
Meteor bundles together jQuery, Handlebars, Node.js, websockets, mongoDB, and DDP and promotes convention over configuration without being a Rails clone.
Tower is an abstraction of top of Express that aims to be a Rails clone.
Geddy is another take on web frameworks.
RailwayJS is a Ruby-on-Rails inspired MVC web framework.
SailsJS is a realtime MVC web framework.
Sleek.js is a simple web framework, built upon express.js.
Hapi is a configuration-centric framework with built-in support for input validation, caching, authentication, etc.
Koa Koa is a new web framework designed by the team behind Express, which aims to be a smaller, more expressive, and more robust foundation for web applications and APIs.

Web Framework Tools:

Jade is the HAML/Slim of the Node world
EJS is a more traditional templating language.
Don't forget about Underscore's template method!

Networking:

Connect is the Rack or WSGI of the Node world.
Request is a very popular HTTP request library.
socket.io is handy for building WebSocket servers.

Command Line Interaction:

Optimist makes argument parsing a joy.
Commander is another popular argument parser.
Colors makes your CLI output pretty.