What is the suggested way to install brew, node.js, io.js, nvm, npm on OS X?

1. Using homebrew install nvm:

   brew update
   brew install nvm
   source $(brew --prefix nvm)/nvm.sh
   

   Add the last command to the .profile, .bashrc or .zshrc file to not run it again on every terminal start. So for example to add it to the .profile run:

   echo "source $(brew --prefix nvm)/nvm.sh" >> ~/.profile
   

   If you have trouble with installing nvm using brew you can install it manually (see here)

2. Using nvm install node or iojs (you can install any version you want):

   nvm install 0.10
   # or
   nvm install iojs-1.2.0
   

3. npm is shipping with node (or iojs), so it will be available after installing node (or iojs). You may want to upgrade it to the latest version:

   $ npm install -g npm@latest
   

   UPD Previous version was npm update -g npm. Thanks to @Metallica for pointing to the correct way (look at the comment bellow).

4. Using npm install ionic:

   npm install -g ionic
   

5. What about ngCordova: you can install it using npm or bower. I don't know what variant is more fit for you, it depends on the package manager you want to use for the client side. So I'll describe them both:

   1. Using npm: Go to your project folder and install ng-cordova in it:

      npm install --save ng-cordova
      

   2. Using bower: Install bower:

       npm install -g bower
      

      And then go to your project folder and install ngCordova in it:

       bower install --save ngCordova
      

PS

1. Some commands may require superuser privilege
2. Short variant of npm install some_module is npm i some_module

2019 update: Use NVM to install node, not Homebrew

In most of the answers , recommended way to install nvm is to use Homebrew

Do not do that

At Github Page for nvm it is clearly called out:

Homebrew installation is not supported. If you have issues with homebrew-installed nvm, please brew uninstall it, and install it using the instructions below, before filing an issue.

Use the following method instead

curl -o- https://raw.githubusercontent.com/creationix/nvm/v0.33.11/install.sh | bash

The script clones the nvm repository to ~/.nvm and adds the source line to your profile (~/.bash_profile, ~/.zshrc, ~/.profile, or ~/.bashrc).

And then use nvm to install node. For example to install latest LTS version do:

nvm install v8.11.1

Clean and hassle free. It would mark this as your default node version as well so you should be all set

I'm using n (Node version management)

You can install it in two ways

brew install n

or

npm install -g n

You can switch between different version of node and io. Here's an example from my current env when I call n without params:

$ n

  io/3.3.1
  node/0.12.7
  node/4.0.0
  node/5.0.0
ο node/5.10.1