Registered developers can download the watchOS 3.2.3 update through the Apple Watch app on the iPhone by going to General -> Software Update. To install the beta, the Apple Watch must have 50 percent battery, it must be placed on the charger, and it needs to be in range of the iPhone.
watchOS betas are only available to developers because there's no way to downgrade the software on an Apple Watch, so non-developers will need to wait for the public release to get the update.
We don't yet know what's included in watchOS 3.2.3, but as a minor 3.x.x update, it likely focuses on minor bug fixes, performance improvements, and security enhancements. We'll update this post should anything be discovered in the first beta.
This is likely to be one of the last updates to the watchOS 3 operating system, as Apple is set to debut new watchOS software at the Worldwide Developers Conference in June.