Update doc

Author: MarkusSintonen

docs/network-backends.md

@@ -73,8 +73,29 @@ while True:
 
 If we're working with an `async` codebase, then we need to select a different backend.
 
-The `httpcore.AnyIOBackend` is suitable for usage if you're running under `asyncio`. This is a networking backend implemented using [the `anyio` package](https://anyio.readthedocs.io/en/3.x/).
+These `async` network backends are available:
+- `httpcore.AsyncioBackend` This networking backend is implemented using Pythons native `asyncio`.
+- `httpcore.AnyIOBackend` This is implemented using [the `anyio` package](https://anyio.readthedocs.io/en/3.x/).
+- `httpcore.TrioBackend` This is implemented using [`trio`](https://trio.readthedocs.io/en/stable/).
 
+Currently by default `AnyIOBackend` is used when running with `asyncio` (this may change).
+`TrioBackend` is used by default when running with `trio`.
+
+Using `httpcore.AsyncioBackend`:
+```python
+import httpcore
+import asyncio
+
+async def main():
+    network_backend = httpcore.AsyncioBackend()
+    async with httpcore.AsyncConnectionPool(network_backend=network_backend) as http:
+        response = await http.request('GET', 'https://www.example.com')
+        print(response)
+
+asyncio.run(main())
+```
+
+Using `httpcore.AnyIOBackend`:
 ```python
 import httpcore
 import asyncio