下記を参考にDockerでDjangoの環境構築するかーと思ったところ少し詰まったのでメモ程度に残します。
https://docs.docker.jp/compose/django.html

docker-compose up -d でコンテナ立ち上げ用としたところDBのコンテナだけうまく立ち上がらず...

toruchan:~/work/py-work$ docker-compose up -d
Starting pywork_db_1 ...
Starting pywork_db_1 ... done
Creating pywork_web_1 ...
Creating pywork_web_1 ... done

toruchan:~/work/py-work$ docker-compose ps
    Name                  Command               State            Ports
-------------------------------------------------------------------------------
pywork_db_1    docker-entrypoint.sh postgres    Exit 1
pywork_web_1   python3 manage.py runserve ...   Up       0.0.0.0:8000->8000/tcp

toruchan:~/work/py-work$ docker-compose logs
Attaching to pywork_web_1, pywork_db_1
db_1   | Error: Database is uninitialized and superuser password is not specified.
db_1   |        You must specify POSTGRES_PASSWORD to a non-empty value for the
db_1   |        superuser. For example, "-e POSTGRES_PASSWORD=password" on "docker run".
db_1   |
db_1   |        You may also use "POSTGRES_HOST_AUTH_METHOD=trust" to allow all
db_1   |        connections without a password. This is *not* recommended.
db_1   |
db_1   |        See PostgreSQL documentation about "trust":
db_1   |        https://www.postgresql.org/docs/current/auth-trust.html
db_1   | Error: Database is uninitialized and superuser password is not specified.
db_1   |        You must specify POSTGRES_PASSWORD to a non-empty value for the
db_1   |        superuser. For example, "-e POSTGRES_PASSWORD=password" on "docker run".
db_1   |
db_1   |        You may also use "POSTGRES_HOST_AUTH_METHOD=trust" to allow all
db_1   |        connections without a password. This is *not* recommended.
db_1   |
db_1   |        See PostgreSQL documentation about "trust":
db_1   |        https://www.postgresql.org/docs/current/auth-trust.html

どうやらパスワードの設定がされていないとエラーになるらしい...？

そこで思いついたのは下記2つ

パスワード設定を無効化
パスワードを設定

とりあえずローカル環境で立ち上げたいだけだし1のパスワード無効化を選択

1の場合の対応方法としてdocker-compose.ymlファイルにPOSTGRES_HOST_AUTH_METHOD: 'trust'の一行を追記
全体としてはこんな感じに

version: '3'

services:
  db:
    image: postgres
    environment:
      POSTGRES_HOST_AUTH_METHOD: 'trust'
  web:
    build: .
    command: python3 manage.py runserver 0.0.0.0:8000
    volumes:
      - .:/code
    ports:
      - "8000:8000"
    depends_on:
      - db

これでコンテナ立ち上げ直したらいけた
後ほどパスワードはちゃんと設定しようと思う...