This is my third, and because I haven't seen an instructables about how to do it, I decided i would post about it.
For this you will need:
A small sheet of plywood or scrap. (I used 3/8th" which was definitely overkill and cost me a jigsaw blade)
An image that you want to make into a puzzle,
A few extra blades,
A little bit of patience
I got my jigsaw (also known as a scroll saw) to do simple work with aluminium, using it as a cheap alternative to a bandsaw. besides needing to frequently replace the blades, it has slowly won me over by being able to cut tight curves and by the smaller kerf size(more on kerf later).
Step 1: Gluing Down the Image
Spray adhesive isn't necessary, any glue that will hold the paper to the wood is alright. I prefer spray adhesive because it lets me finish this first step in two minutes, rather than requiring me to put down the project for an hour.
Print your image at the size you want, and line it up on the scrap so that your entire image, and however much background you want is over the scrap of wood. You will trim the paper and the scrap in the next step so don't worry about it yet.
Next glue your image to the plywood backing. I had a lot of room on this scrap for this image so I just sprayed a bit of the adhesive on the wood and then pressed the backing down onto it with enough room on all sides for the background.
Step 2: Cutting the Border
So far I haven't done a traditional border yet and you can be creative about these too. Your border can be any shape that you can cut on the jigsaw, so have fun with this.
I just gave a lot of white space to the robot because I wanted to show you some fancy things about cutting the pieces on the inside. I could just as well have cut only the robot out leaving no background, or cut a pattern in the background to make things interesting.
Step 3: Piece Cutting Practice
Cut the interlocking pieces as big as you have to to get them to work. The blades turn very tightly, and produce a relatively small kerf (the thickness of the notch cut by the blade) especially if you maintain a slight forward pressure on the workpiece to keep it engaged with the teeth of the blade as you turn it.
the interlocking piece in the photo is about 1/2 and is one of the larger ones in the puzzle"
Once you get one to work cut a few more like it and practice different variations as you go. Though you are only working with scraps try to cut one piece free at a time so that you can use the relatively large scrap to control the relatively small pieces you are making. Remember, you don't need all adjacent pieces to have a successfully interlocking part. In fact, many of the internal linkages in this puzzle are unsuccessful, but I took extra care around the border so that the puzzle wouldn't fall apart while pushed around the table.
Step 4: Cutting the Puzzle
Remember what you learned from practicing earlier and go ahead and cut the puzzle out.
It's best if you dont mark them and just cut freehand.
Make sure none of the pieces are supported by impossibly slender pieces of wood.
Make sure that the puzzle has at least a few functional interlocks so that it won't fall apart if pushed around
Try to keep the grain (the size of pieces and frequency of interlocks) even throughout the puzzle. Although there are a few exceptions to this rule, try to make sure it isn't clear which side you started cutting on, just by looking at how the piece size and the number of interlocks begins to dwindle as you get tired. This should be fun, if you are getting tired go take a break and come back when you want to.
Unlike most of the cardboard puzzles, methodically stamped by an unseeing machine, your puzzle will be cut while you can see the patterns and the edges in the picture you are making into a puzzle. Go wild, cut along the edges of interesting features, while doing this you could but dont have to add an occasional interlock. If your puzzle will have some relatively large solid color areas, dont cut normal boring pieces in there, make shapes like circles, squares, stars or hearts.
Once you are done cutting you are done, sit back and enjoy putting it together, or letting someone else put it together.