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

apt-get update
apt-get install ca-certificates curl gnupg lsb-release -y
 
mkdir -p /etc/apt/keyrings
curl -fsSL https://download.docker.com/linux/debian/gpg | gpg --dearmor -o /etc/apt/keyrings/docker.gpg
 
echo \
  "deb [arch=$(dpkg --print-architecture) signed-by=/etc/apt/keyrings/docker.gpg] https://download.docker.com/linux/debian \
  $(lsb_release -cs) stable" | tee /etc/apt/sources.list.d/docker.list > /dev/null
 
apt-get update
apt-get install docker-ce docker-ce-cli containerd.io docker-compose-plugin -y

on kali the apt source needs to be manually edited to debian bookworm

#testing out
docker run hello-world

‼ This is basically equivalent to sudo rights! Be careful!

sudo groupadd docker
sudo usermod -aG docker $USER

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

sudo apt-get install ca-certificates curl gnupg lsb-release
curl -fsSL https://download.docker.com/linux/ubuntu/gpg | sudo gpg --dearmor -o /usr/share/keyrings/docker-archive-keyring.gpg
echo \
  "deb [arch=$(dpkg --print-architecture) signed-by=/usr/share/keyrings/docker-archive-keyring.gpg] https://download.docker.com/linux/ubuntu \
  $(lsb_release -cs) stable" | sudo tee /etc/apt/sources.list.d/docker.list > /dev/null
sudo apt update
sudo apt-get install docker-ce docker-ce-cli containerd.io docker-compose-plugin -y

First install WSL according to the docs: https://docs.microsoft.com/de-de/windows/wsl/install-manual, then install docker Desktop as admin.

If the user is not admin, its needs to be added to a Group