Document usage of library

- Add a better summary
- Add example usage
- Add example output

README.md

@@ -6,11 +6,72 @@
 [![Known Vulnerabilities](https://snyk.io/test/github/cisagov/cyhy-logging/develop/badge.svg)](https://snyk.io/test/github/cisagov/cyhy-logging)
 
 This is a Python package that provides a standard logging configuration which is
-used by the Cyber Hygiene system.
+used by the Cyber Hygiene (CyHy) system.
 
-## Usage ##
+The logging setup uses the
+[`RichHandler`](https://rich.readthedocs.io/en/stable/logging.html) to provide
+visually appealing and informative log outputs, including enhanced tracebacks
+when debugging.  Additionally, default filters like the
+[`RedactPasswordFilter`](src/cyhy_logging/log_filters.py) are applied to all log
+handlers to automatically filter and redact sensitive information.
 
-<!-- TODO: add usage -->
+To ensure that all logs across different parts of the CyHy system are properly
+grouped under a single root, the `CYHY_ROOT_LOGGER` constant is used. By using
+this constant when configuring loggers (`CYHY_ROOT_LOGGER` as the root logger),
+all log messages are consistently organized under the same logging namespace,
+which simplifies log management and makes it easier to locate all related logs.
+Additionally, using `CYHY_ROOT_LOGGER` allows the verbosity of CyHy logs to be
+increased independently without affecting the verbosity of other packages that
+use the logging system.
+
+## Example Usage ##
+
+```python
+from cyhy_logging import CYHY_ROOT_LOGGER, setup_logging
+import logging
+
+# Set up logging
+logger = logging.getLogger(f"{CYHY_ROOT_LOGGER}.{__name__}")
+setup_logging("DEBUG")
+
+# Use the logger
+logger.debug("This is a debug message")
+logger.info("This is an info message")
+logger.warning("This is a warning message")
+logger.error("This is an error message")
+logger.critical("This is a critical message")
+
+# The logger will redact sensitive information by default
+logger.info("Logging into database at https://admin:[email protected]/secret")
+
+# Raise an exception to demonstrate the enhanced traceback
+raise Exception("This is an exception")
+
+# Shutdown logging
+logging.shutdown()
+```
+
+## Example Output ##
+
+```console
+[13:37:28] DEBUG    This is a debug message                   <python-input-0>:9
+           INFO     This is an info message                  <python-input-0>:10
+           WARNING  This is a warning message                <python-input-0>:11
+           ERROR    This is an error message                 <python-input-0>:12
+           CRITICAL This is a critical message               <python-input-0>:13
+           INFO     Logging into database at                 <python-input-0>:16
+                    https://admin:****@example.com/secret
+╭───────────────────── Traceback (most recent call last) ──────────────────────╮
+│ in <module>:18                                                               │
+│ ╭───────────────────────────────── locals ─────────────────────────────────╮ │
+│ │ CYHY_ROOT_LOGGER = 'cyhy'                                                │ │
+│ │           logger = <Logger cyhy.__main__ (DEBUG)>                        │ │
+│ │          logging = <module 'logging' from                                │ │
+│ │                    '/Users/lemmy/.pyenv/versions/3.13.0/lib/python3.13/… │ │
+│ ╰──────────────────────────────────────────────────────────────────────────╯ │
+╰──────────────────────────────────────────────────────────────────────────────╯
+Exception: This is an exception
+```
 
 ## Contributing ##