If you're using OS X or Windows, the best way to install Node.js is to use one of the installers from nodejs.org. If you're using Linux, you can use the installer, or you can check NodeSource's binary distributions to see whether or not there's a more recent version that works with your system.
Test: Run node -v. The version should be higher than v0.10.32.
Node comes with npm installed so you should have a version of npm. However, npm gets updated more frequently than Node does, so you'll want to make sure it's the latest version.
sudo npm install npm -g
Test: Run npm -v. The version should be higher than 2.1.8.
For more advanced users.
The npm module is available for download at https://registry.npmjs.org/npm/-/npm-{VERSION}.tgz.