I've repaired many a broken object, and not always very well, but I have found 2 ways that work very well.
Superglue and paper, sort of like paper mache where you glue strips of paper together to make an object. Instead of paste, use super glue. You can use tissue paper, newspaper, cardboard, or whatever you have handy. Its important that the paper be absorbant enough to soak the superglue, and flexible enough to form around your object. Ive done this sort of patching many times, but I havent really taken many photos of it.
I have an old drill, in an impressive accident, he stepped on, and broke my drill in half (It was quite remarkable, Im sure he couldnt do it again if he tried.) I tried the old superglue and paper mache type repair (shown in the couple images), It seem to work great, until the first time that I tried pulling a deck screw out, and it snapped in half right where I repaired it. I had recently been using bondo, and thought it might work better. I used the metal mesh included for extra reinforcement. I slathered it on pretty thick on the outside, but was a bit more careful on the inside, because I had to be able to put the parts back inside it, and close it up. It turned out quite well, and has held up to regular use like a champ. Its pretty ugly, but It still works, and thats the important thing.
The next set of 3 photos after the drill (orange), is a plastic cowl part for my car. It broke, and replacements are hard to find. I wanted some metal reinforcement to make the repair sturdy, otherwise it would likely break again. I took a metal can out of recycling, cut out a bit of it, nailed some holes into it for the bondo to form around, bent it to fit the repair location, and gobbered it up with some bondo, pressed the metal into it, and gobbered a bit more bondo around it, and let it set. Its an ugly repair, but since the repair is on the underside, nobody knows its there (until now!)
The last set of pictures is on a car, which is what this stuff is intended for, auto body repairs. I had stripped the paint off this car, and was surprised to find a whole lot of bondo on the car. After I removed the paint, the bondo came off with it. Later I cleaned up the bare metal, and found that I was going to have to learn now to do some body work. Most of it was pretty easy, just time consuming, but when I got to a tricky part, I had to figure something out. The gas door area was pretty well smashed in, and pulled out, welded up, and looked horrible. I needed a way to put the bondo on, without making too much mess, its a lot of work to remove excess bondo, so you want to put just a little more than you need, or you will end up doing a lot of work removing it. I found out that the bondo doesnt stick to aluminum foil tape very well, so I took some cardboard from a box, wrapped aluminum foil tape around it, and fit it in the gap between the fender, and gas door. Then I was abte to pack in the bondo all around the gas door, without messing up the gas door hole. After the bondo set up, I pulled out the cardboard, and only had a small edged to clean up to look like it came from the factory. The aluminum foil tape made a nice surface that the bondo doesnt stick to very well, and the cardboard held the shape that I wanted very well, making a difficult job, easy.
Bondo is a brand name for auto body filler, any filler will do, its just a fiberglass epoxy that you mix up, and it hardens in a few minutes, and cures in a few hours. You can use auto body filler to create new objects too, its fairly inexpensive, durable, sandable, and paintable.