update
You have node + npm installed. By default npm uses /usr/lib/node_modules/ directory to install global modules. Non-priveledged users normally don't have write access to that directory and as such, cannot install npm packages globally.
The command echo prefix = ~/.node >> ~/.npmrc tells npm to install global packages to ~/.node/node_modules instead of usr/lib/node_modules.
After calling:
echo 'export PATH=$HOME/.node/bin:$PATH' >> ~/.bashrc
all npm packages which provide binary scripts are added to $PATH (e.g. yo, browserify) but also npm.
npm package is managed via npm package manager itself. The following command updates npm to the latest version:
npm install -g npm
previous answer
NodeSource provides a binary build of nodejs + npm.
In usage instructions they say to run both commands as admin for Debian systems:
sudo curl -sL https://deb.nodesource.com/setup | bash -
sudo apt-get install -y nodejs nodejs-legacy
The most important line in the setup script is this:
 echo 'deb https://deb.nodesource.com/node ${DISTRO} main' > /etc/apt/sources.list.d/nodesource.list
node + npm should be installed on your system globally now. Updates should be managed by apt-get from now on.
From what I can tell, you have another node + npm installed in your ~/.node directory. I am not sure why you need it. As far as I know global npm packages are installed into ~/.npm directory and they don't interfere with npm binary installed by apt-get.
In any way, if you really want to use your custom node installation from ~./node/bin, you should export $PATH this way:
export PATH="$HOME/.node/bin:$PATH"
Also you can export $PATH automatically by adding this command to ~/.bashrc file:
echo 'export PATH=$HOME/.node/bin:$PATH' >> ~/.bashrc
*NIX looks for binary files (e.g. npm) in each directory specified in $PATH. It goes from left to right and executes the first matching binary file it finds. Somewhere in $PATH variable you have /usr/bin. If you want to npm / node from ~/.node/bin to be found first, you should put that directory further to left in the $PATH environment variable.