How to add wall panels to file cabinet drawers

You need something like these Heavy Duty Cabinet Hangers:

components http://www.screwmaster.co.uk/ekmps/shops/screwmaster/images/pair-of-heavy-duty-cabinet-hangers-260kg-load-capacity-for-kitchen-wall-units-57-p.jpg

The metal plates at the top screw to the wall, the hook like things in the middle screw to the inside of the cabinet and the plastic covers them up.

in place http://www.screwmaster.co.uk/ekmps/shops/screwmaster/images/pair-of-heavy-duty-cabinet-hangers-260kg-load-capacity-for-kitchen-wall-units-%5B3%5D-57-p.jpg

You do need to cut a hole in the backing for the hook, but the plastic will hide these as well.

Ideally when you set a stand-alone cabinet you have a scribe on both of the ends that contact the wall like so (dimensions are exaggerated for clarity):

Not often are you going to find integral scribes on a store bought vanity but you can add your own after the fact and that gives you the chances to set the piece to the median square of the corner and conform to any hinkyness relative to plum as well. Note the L-shape of the scribe, this gives you a place to run screws and still be able to plane or sand the scribe edge.

Once you've scribed in your cabinet you can set your top, splitting the difference from square so as to maintain the 1" (usually) over hang on the cab. If the gap when split is less than an 1/8" it's probably acceptable to caulk it and then tile around it if you so choose. If the gap is bigger than 1/4" (between an 1/8 and a 1/4 is debatable) you can consider scribing the c-top into place but it will require a diamond grinding wheel and nerves of steel. You may want to consult a professional stone mason on that one. The biggest problem is you're adding scribe to the cabinet and loosing depth and width on your top which is subtracting from your overhang so you'll have to be judicious. Anything less than say a 1/2" of overhang will look odd. It should be noted that this kind of problem would require your wall to be out of square by 1/2" over 30"-36"? depending on your vanity. That's a lot. If that's the case, you might want to consider fixing your walls before you begin setting cabinets. If the problem is just an acute build up of compound in the corner, you may be able to scrape off the mud where needed but if you have to start cutting in to the drywall below the paper, its not worth it. Best of luck!