How do I retrieve the available commands from a module?

Use the parameter -ListAvailable

Get-Module <moduleName> -ListAvailable | % { $_.ExportedCommands.Values }

"<moduleName>" is optional. Omit to show all available modules.

Exported commands are not available if the module is not loaded. You need to load the module first and then execute Get-Command:

Import-Module -Name <ModuleName>
Get-Command -Module <ModuleName>