Yes you can run Docker on any Linux distro. These steps listed below are for Ubuntu Desktop 18 LTS. You can find the full official docs and steps for other Linux distributions here:
Ubuntu: https://docs.docker.com/install/linux/docker-ce/ubuntu/
Fedora: https://docs.docker.com/install/linux/docker-ce/fedora/
CentOS: https://docs.docker.com/install/linux/docker-ce/centos/
Debian: https://docs.docker.com/install/linux/docker-ce/debian/
Installing Docker
The Docker docs suggest setting up a Docker repository to install and update from.
This is where you should start:
https://docs.docker.com/install/linux/docker-ce/ubuntu/#set-up-the-repository
After completing the installation steps, test out Docker:
sudo docker run hello-world
This should download and run the test container printing "hello world" to your console.
Installing Docker Compose
Unlike the Mac and Windows Docker Desktop versions, we must manually install Docker Compose. See the instructions for the installation steps (Click on the tab for Linux)
https://docs.docker.com/compose/install/#install-compose
After completing, test your installation:
docker-compose -v
This should print the version and build numbers to your console.
Run without Sudo
Follow these instructions to run Docker commands without sudo:
https://docs.docker.com/install/linux/linux-postinstall/#manage-docker-as-a-non-root-user
The docker group will likely already be created, but you still need to add your user to this group.
Start on Boot
Follow these instructions so that Docker and its services start automatically on boot:
https://docs.docker.com/install/linux/linux-postinstall/#configure-docker-to-start-on-boot
You may need to restart your system