Couple references to derive below instructions for Ubuntu 18.04 (not tested):
https://www.digitalocean.com/community/tutorials/how-to-install-and-use-docker-on-ubuntu-18-04
https://phoenixnap.com/kb/install-docker-compose-ubuntu
Release 1.25.4 · docker/compose · GitHub
From that would be:
sudo apt update
sudo apt upgrade
sudo apt install apt-transport-https ca-certificates curl gnupg-agent software-properties-common
curl -fsSL https://download.docker.com/linux/ubuntu/gpg | sudo apt-key add -
sudo add-apt-repository "deb [arch=amd64] https://download.docker.com/linux/ubuntu $(lsb_release -cs) stable"
sudo apt update
sudo apt install docker-ce
sudo usermod -aG docker $USER
sudo curl -L "https://github.com/docker/compose/releases/download/1.25.4/docker-compose-$(uname -s)-$(uname -m)" -o /usr/local/bin/docker-compose
sudo chmod +x /usr/local/bin/docker-compose