Making your Xap available to the City as a custom tool is easy. First you need to publish your xap so that it is available via a public url. This is covered at the end of the part 1 xap-building tutorial that's accessible via the Learn menu:

Once the xap has been published, you simply log into the city as an administrator and add a tool, as shown below, that points to the xap url:

Because the xap url can contain a link to a specific version of the xap, you can create multiple tools in the City that all point to the same xap, but to different versions of it - allowing you to release a beta version alongside the stable production version. By using the conditional access control feature on City tools, you can control who has access to the beta: