Apple has just released the first update to the Watch software, version 1.0.1.

Details of how to update are given here.

The simple and safe procedure is:

1. Put your Watch on charge. Leave it on charge until it has at least 50% battery to run.
2. Ensure that your paired iPhone is close (so in range of the Watch), is connected to WiFi, and connect it to its charger.
3. Open the Watch app on the iPhone.
4. Open My Watch in that App.
5. Tap General, then Software Update.

You will then see the download and install screen.

This update contains a long list of security and other bug fixes.