The following works on Raspbian Jessie…
Install Node JS 6:
curl -sL https://deb.nodesource.com/setup_6.x | sudo -E bash -
sudo apt-get install -y nodejs
Install the Node JS build tools if required:
sudo apt-get install -y build-essential
Check it’s working:
node -v
npm -v
Update
Apparently this only works for ARMv7 and later processors, so this doesn’t work on Raspberry Pi first generations and Zeros.
To install on these, first get the URL to the version you want from https://nodejs.org/dist/ (Latest is always https://nodejs.org/dist/latest/).
Download and extract the package, eg:
wget https://nodejs.org/dist/latest/node-v7.10.0-linux-armv6l.tar.xz
tar -xJf node-v7.10.0-linux-armv6l.tar.xz
cd node-v7.10.0-linux-armv6l
Copy the files to /usr/local:
sudo cp -R * /usr/local/
/usr/local/bin should already be in the path so it should just work.
node -v
npm -v