1. The standard way to inject services in other services is passing dependencies directly through the constructor:

mymodule.services.yml:

    services:
      mymodule.foo_service:
        class: Drupal\mymodule\FooService
        arguments: ['@current_user']

2. While you can define a factory method in *.services.yml, see https://symfony.com/doc/current/service_container/factories.html, in Drupal the most common places for this are Controllers and Plugins which implement ContainerInjectionInterface::create or ContainerFactoryPluginInterface::create. See How do I use dependency injection on \Drupal::moduleHandler() to a Controller?

3. \Drupal::service... is largely used from procedural code when not in an OOP context, like hooks are static callbacks. See the comment from @Kevin.

1. The standard way to inject services in other services is passing dependencies directly through the constructor:

mymodule.services.yml:

    services:
      mymodule.foo_service:
        class: Drupal\mymodule\FooService
        arguments: ['@current_user']

2. While you can define a factory method in *.services.yml, see https://symfony.com/doc/current/service_container/factories.html, in Drupal the most common places for this are Controllers and Plugins which implement ContainerInjectionInterface::create or ContainerFactoryPluginInterface::create. See How do I use dependency injection on \Drupal::moduleHandler() to a Controller?

3. \Drupal::service... is largely used from procedural code when not in an OOP context, like hooks or static callbacks. See the comment from @Kevin.