Instructions for installing Docker can be found on the manufacturer's site. For Debian / Ubuntu, I did the installation as follows.

Debian / Ubuntu

For a brand new Debian release, docker-ce may not yet be available as "stable", by adding edge test, docker-ce can still be installed:

sudo add-apt-repository \
   "deb [arch=amd64] https://download.docker.com/linux/ubuntu \
   $(lsb_release -cs) \
   stable edge test"

Debian and Ubuntu have different sources here: For Ubuntu I had to use https://download.docker.com/linux/ubuntu instead of https://download.docker.com/linux/debian.

To remove the repository for Debian again, the following command can be used:

sudo add-apt-repository --remove \
   "deb [arch=amd64] https://download.docker.com/linux/debian \
   $(lsb_release -cs) \
   stable"

Docker-compose

Docker-compose allows multiple Docker containers to be stored in a common docker-compose.yml file, allowing them to be launched or upgraded together. Docker-compose can be added with the following commands:

sudo curl -L "https://github.com/docker/compose/releases/download/1.28.4/docker-compose-$(uname -s)-$(uname -m)" -o /usr/local/bin/docker-compose
sudo chmod +x /usr/local/bin/docker-compose

see: https://docs.docker.com/compose/install/

Instructions for the following platforms

For the following platforms, there is a corresponding Docker installation guide on the vendor site:

• Docker Desktop for Mac (macOS)
• Docker Desktop for Windows
• CentOS
• Debian
• Fedora
• Raspbian
• RHEL
• SLES
• Ubuntu
• Binaries

Source: https://docs.docker.com/engine/install/