There are a number of techniques. If you don't mind using chemical treatments, there is Apistan, Checkmite plus, oxalic acid, etc., etc. Then there is also the powdered sugar dusting method.
If it is really weak and you have another colony, you could always combine the two. But you are still going to have a mite problem that is going to kill your bees, if you don't do something. Then again, if you don't do anything, your problem will cure itself. But your bees will be dead to. Sorry if this is too blunt.
Just because something is new to you, doesn't mean it is new, or revolutionary. Mark Berninghausen