How do I move layered navigation to the right sidebar?

If you are using Improved Layer Navigation, please use "Left" placeholder in the admin and move the layered navigation block to the right side in the module layout. To do that, open that file

app/design/frontend/<PACKAGE>/<THEME>/layout/amasty/amshopby.xml  :

and replace this

        <reference name="left">

with this

       <reference name="right">

For more flexible Magento sidebar navigation menu settings, check out new Amasty solution - Magento 2 Layered Navigation.