Ideas to finish the edge of my wall with decorative stone
I'd install some wooden trim / decorative moulding and paint it to match nearby woodwork.

 





Make the left vertical edge of the decorative-stone even by cutting where needed (e.g. middle row of upper photo). 
tack/glue appropriate sized stripwood behind front edge of moulding as shim. 
Attach the shimmed moulding using adhesive (as presumably used for the decorative-stone) 
Paint


(I'd also grout all those stepped joints)



Another option is to continue the decorative-stone a short way around the corner - some manufacturers of these types of panels allow for this. (random example)