If I wanted to host a LightSwitch application on my home computer, what would I need to do? My home computer has a Verizon FIOS connection. What software, configuration, etc. would I need?
I assume you mean a 3 tier web/silverlight LightSwitch application. This is just like any other Silverlight app - all you will need on your home computer is IIS (to host the website and services) and your data source (eg. SQL Server). Check out the "Publish application wizard."
Take a look at How to: Deploy a LightSwitch Application for details.
From the article -
Once published, a .zip file that contains the package is placed in the directory that you specified for the publish output. Once this package has been created, a server administrator can use the MSDeploy tool to deploy the application to Internet Information Services (IIS) and SQL servers. The administrator can open inetmgr, and move to the location where the application will be deployed. The administrator can then right-click the location and select Deploy: Import Application. The result is a wizard which the administrator can run to deploy the application.