Sharepoint - PowerShell - create list from list template in list template gallery
you can get the built in list templates using the SPListTemplateType enumeration:
$listTemplate = [Microsoft.SharePoint.SPListTemplateType]::Contacts
if you want to access custom list templates saved as STP files on your site, you have to fetch them from your sites list templates and access them through the list name:
$site = Get-SPSite http://site
$listTemplates = $site.GetCustomListTemplates($web)
$web.Lists.Add("Your new list", "", $listTemplates["ListTemplateName"])
you can also save these list templates using SaveAsTemplate() method on a given SPList object.