Step by step

Build Docker images for FastAPI and for PostgreSQL

docker build -t fastapi-image -f Dockerfile.fastapi .

docker build -t postgres-image -f Dockerfile.postgresql .

Build container and use it

docker-compose build

docker-compose up

Check if it's working

Start fastapi container

docker-compose exec fastapi sh

Run python

python

Try to connect to PostgreSQL

import psycopg2
conn = psycopg2.connect(host="postgres", port=5432, dbname="fastapi_db", user="admin", password="password")