I'm using Windows as a simple user (I don't have any admin rights) and want to install NodeJS LTS.
On the download site I have the choice to download only the binary node.exe (which don't includes npm) or the node.msi installer which requires the admin rights to execute.
How can I manually install node.exe and also be able to use npm?
On Node's download page referenced in step 1. there is now a .zip archive download which contains both the nodejs executable and npm. Unpacking that to a suitable path and adding this path to your PATH environment variable (step 2.) will give you both node and npm (so you can skip steps 3. - 6.).
Let say you want to install it into %userprofile%\Applications\nodejs-lts, let's name it <NODE_PATH>.
Download the LTS node.exe binary for Windows and copy it to <NODE_PATH>.
Add <NODE_PATH> to your PATH environment variable (set PATH=<NODE_PATH>;%PATH% or using Windows user interface)
Download the stable at https://registry.npmjs.org/npm/-/npm-{VERSION}.tgz npm package (following the documentation)
Unzip the npm-{VERSION}.tgz anywhere (using 7zip for example)
Launch a cmd and cd into the place where you have unzipped npm
Execute: node cli.js install -gf or node bin/npm-cli.js install npm -gf on certain versions (thanks to this comment)
The last command is specified in the Makefile for target install, target which the README.md invites to execute when manually installing.