Xamarin currently offers VS integration only for the Business or Enterprise editions, the Free tier has no support for VS. You can however use a trial version of Xamarin (Bussiness or Enterprise) for about 30 days that will let you build iOS and Android apps with some limitations (the built executable has a limited life time, one day I think). After 30 days you can buy a Xamarin license or the tool will revert to the Free Xamarin tier (this one is severely limited - application size, integration with external libraries and so on).
According to this video http://channel9.msdn.com/Events/Visual-Studio/Connect-event-... Xamarin (Bussiness or Enterprise) should work just fine with VS Community.