Inevitably you will at some point in your career damage a customer's stuff.  Most common is usually the appliance you are working on, or the floor.  The big stuff is flooding a customer's house, fire, smoke, etc.  

Let's talk about the small stuff first.  

Scratched/ damaged appliance:  Just understand that your maximum liability on this is the value of the appliance.  Not the cost to replace.  The value of a 10 year old used appliance.  If you did the damage the first thing you should do is own it.  Second, and most important: Dont ever talk about insurance or compensation etc.  Once you start planting ideas in the customer's head, there is no turning back.   For example: you broke a crisper bucket during removal.  All you need to say is "your crisper bucket broke during disassembly, do you want me to order you a new one? The cost is X.XX.  Its not so much you want them to pay for the bucket, its more so that you are conveying that you did not just F* up. Normal course of things.  If you arent that brave, just tell the customer what you did and that you will bring back another one in a few days. 

You dented the door: Say to the customer: "How do you want to resolve this?" You really need to smear on the humility.  Call yourself and idiot, etc.   The goal is to build empathy, and avoid the adversarial confrontation.   You will be surprised how often they say don't worry about it.  Sometimes they ask for a discount, some will ask for a new door.  If they ask for a door, look it up right there, on the spot.  Figure out the cost of the door, write the lady a check on the spot for the door + $150 for someone else to install it.   Its not your problem that the door is NLA, I can almost guarantee you they will just pocket the money and buy a fifty cent magnet.  The important part is to settle the matter right then and there.  Write the check, or discount the bill, you need to specifically write that you are fully compensating them for the damage to the door.  Make them sign.  

The damaged flooring:  This is one where most of you will throw your hands up and file a claim.  I have been in the appliance business for 20+ years and I can shamefully tell you I have (my delivery guys really) damaged many floors, doors, windows, walls, cars, and more.  If you damage a floor, do not get the customer involved.  Its your mess, you clean it up.  If you tell the customer to go get an estimate, you will end up buying Karen a new floor.   Most flooring damage is in the way of a dent, and some more severe have a dent/ minor scratch.  A good steam mop will pull 99% of dents out.  If there is a scratch, buff it out with a bit of floor polyurethane and a rag.  The trick to resolving this in my experience is to do the entire kitchen.  Just steam/ clean, not POLY) Steam ALL of her dents out ,and get an excellent hardwood floor cleaner (like BONA) and clean her floors.  Leave her the cleaner as a parting gift.  When you see the customer's eyes get big, or crack a smile, not only did you dodge an expensive bullet, but you get to keep the customer.  

 YOU change the window, YOU (or YOUR contractor) fix the wall/paint/trim.  Your people will look out for you, and generally will give you an excellent price for the correction.  Your customer's contractor will get paid big time. 

If you break a ceramic tile: If you break a tile its either you were Grossly negligent, or the floor was installed incorrectly.  Buy the closest thing you can find, but DO NOT install that tile in front of the stove/ fridge.  Its likely not an exact match and will look out of place.  Harvest a tile from under the fridge or stove and install that tile, putting the new tile out of sight.  

Water damage- wood flooring:  If you catch it within a couple weeks you should be fine.  Wood swells up when wet, and will always shrink when dry.  Solve the leak, apologise profusely, and get to drying it.  Hair dryers, towels, and a few trips will take care of it.  

Water damage drywall:  Hire a contractor, tell him to take care of it 100%, AND SEND YOU THE BILL.  

WHY BOTHER, I HAVE INSURANCE FOR THIS?   Your insurance will cover the first claim, and I promise at your renewal you rates will skyrocket IF they even take you back.  If you file 2 claims in about 5 years, not only will your insurance co drop you, but good like finding anyone to cover you.   If you do some BIG damage, like massive flooding or fire/ smoke, that is what insurance is for. 

It really boils down to this:  You can fix a scratched floor for a few hundred dollars.  Once you get insurance, the customer, and random contractors involved, it instantly becomes a four figure repair. You will end up paying for all of it one way or another.