This is based on official documentation but is simplified just for what I needed and hopefully is useful for you also.

1. Check debian version (in this case it is 10.8 - buster)

# cat /etc/debian_version 
# lsb_release -cs

2. Remove any existing docker installation (older versions that came with the OS, etc.)

NOTE: if nothing is removed, no problems.

# apt remove docker docker-engine docker.io containerd runc

3. Add the official GPG key

# curl -fsSL https://download.docker.com/linux/debian/gpg | gpg --dearmor -o /usr/share/keyrings/docker-archive-keyring.gpg

4. Add docker repository to apt

NOTE: if in your case the lsb_release command does not provide the desired outout, you need to check yoursefl which version you have and replace $(lsb_release -cs) with the hardcoded value (e.g. buster, stretch, or whatever).

# echo "deb [arch=amd64 signed-by=/usr/share/keyrings/docker-archive-keyring.gpg] https://download.docker.com/linux/debian \
   $(lsb_release -cs) stable" | tee /etc/apt/sources.list.d/docker.list > /dev/null
# cat /etc/apt/sources.list.d/docker.list

5. Run apt update

NOTE: important to run this command because if not, the next one will not install anything.

# apt update

6. Instal docker with apt

# apt install docker-ce docker-ce-cli containerd.io

And done: docker is installed. Run the following to check

# docker container ls
# ps -ef |grep -i docker

Video format of this tutorial

Links

Official documentation: https://docs.docker.com/engine/install/debian/