There are several commands that may require you to pass in a SharePoint Content Database ID. PowerShell makes it easy, just use the Get-SPContentDatabase command.
Pass in the WebApplication Parameter to get a list of all of your Content Databases for that Web Application:
Need to know the Content Database of a specific site (web)? Just pass in the site parameter:
For a complete list of SharePoint 2010 Content Database Powershell cmdlets go to http://technet.microsoft.com/en-us/library/ee890116(office.14).aspx