Update for 2024

Since this question was posted, version 20 became the newest LTS version. So Ahmed Boutaraa's answer was correct for the version 14 part of the question, but people stumbling on this question may be seeking the most recent LTS. If you follow those instructions, you will be stuck in version 14.

Luckily, NodeSource also provides an installation script that installs the current LTS rather than a specific version. That should make this answer a bit more future-proof. You can also get the same info straight from the source.

As an aside, there is a script called nvm that is great for managing your node version. It makes it easy to install multiple versions, like if you work with multiple projects with different version requirements or if you want to experiment with the latest version and easily switch back to LTS for regular work. You can find installation instructions on their repository.

How to install the latest LTS version

This set of instructions will install whatever version is the latest LTS version. When a new version is released, you may have to run these instructions again to pull the new install script for the new version.

# As a user with sudo
curl -fsSL https://deb.nodesource.com/setup_lts.x | sudo -E bash -
sudo apt-get install -y nodejs

# OR as root
curl -fsSL https://deb.nodesource.com/setup_lts.x | bash -
apt-get install -y nodejs

How to install the latest non-LTS version

This set of instructions will install whatever version is the latest non-LTS version. When a new version is released, you may have to run these instructions again to pull the new install script for the new version.

# As a user with sudo
curl -fsSL https://deb.nodesource.com/setup_current.x | sudo -E bash -
sudo apt-get install -y nodejs

# OR as root
curl -fsSL https://deb.nodesource.com/setup_current.x | bash -
apt-get install -y nodejs

How to lock into v21 (latest, for now)

# As a user with sudo
curl -fsSL https://deb.nodesource.com/setup_21.x | sudo -E bash -
sudo apt-get install -y nodejs

# OR as root
curl -fsSL https://deb.nodesource.com/setup_21.x | bash -
apt-get install -y nodejs

How to lock into v20 (current LST)

# As a user with sudo
curl -fsSL https://deb.nodesource.com/setup_20.x | sudo -E bash -
sudo apt-get install -y nodejs

# OR as root
curl -fsSL https://deb.nodesource.com/setup_20.x | bash -
apt-get install -y nodejs

All Platforms (Mac, Linux & Windows) 2024

If you just need to upgrade your old version of Node.js to the latest one and don't need multiple versions, simply over-write your existing executable with the new one.

Download the Latest Node.js from nodejs.org/en/download

This Just Works! ^TM on all platforms and is the easiest/fastest method.
When you run node -v in your terminal you will see the the latest version.

Mac

If you originally installed Node.js using brew then run:

brew upgrade node

Managing Multiple Versions of Node.js:

If you need to run multiple versions of Node.js on your machine e.g. if you have an older project that targets a specific version on AWS Lambda, then NVM (Node Version Manger) is your friend!

Step 1 - Get NVM

curl -o- https://raw.githubusercontent.com/nvm-sh/nvm/v0.39.3/install.sh | bash

If you're curious about the installation command read the source code
... its been reviewed by several node.js security experts

Step 2 - Install the Specific Version of Node.js you need

Once you've got NVM you can install a specific version of Node.js using the nvm command:

nvm install v22.16.0

Note: you may need to close & re-open your terminal window for nvm command to be available.

You should expect to see something like this in your terminal:

Now using node v22.16.0

You now have the latest Node.js on your machine.
And if you need to temporarily switch to a different/previous version, you can do it with a simple nvm command.

Note: avoid using sudo with Node/NPM as it violates the security principal of least privilege

NVM is considered "better" than N for managing multiple Node.js versions because the verbose commands mean it is much easier to keep track of what you are doing in your Terminal/SSH Log. It is used by the team at NPM the creators/custodians of the Node.js World!

Install nodejs v20 on Debian and Ubuntu based distributions

step 1 : Download and import the Nodesource GPG key

sudo apt-get update
sudo apt-get install -y ca-certificates curl gnupg
sudo mkdir -p /etc/apt/keyrings
curl -fsSL https://deb.nodesource.com/gpgkey/nodesource-repo.gpg.key | sudo gpg --dearmor -o /etc/apt/keyrings/nodesource.gpg

step 2 : Create deb repository

NODE_MAJOR=20
echo "deb [signed-by=/etc/apt/keyrings/nodesource.gpg] https://deb.nodesource.com/node_$NODE_MAJOR.x nodistro main" | sudo tee /etc/apt/sources.list.d/nodesource.list

optional: here we are installing nodejs v20 but if you want to install v18 change NODE_MAJOR=18 in above command. Similarly if you want to install nodejs v16 then change NODE_MAJOR=16.

step 3 : Run Update and Install

sudo apt-get update
sudo apt-get install nodejs -y

congratulations you just installed nodejs

To uninstall nodejs

sudo apt-get purge nodejs &&\
rm -r /etc/apt/sources.list.d/nodesource.list &&\
rm -r /etc/apt/keyrings/nodesource.gpg

I solved this problem

rm -rf ~/.nvm
nvm install 16