There are simple and elaborate ways to make your own puzzles, from your own images or drawings.
The easiest way is just to cut up the image in random pieces of whatever shape or size you want. It is probably better to make the pieces the same size, but you can decide otherwise. However, this method will likely result in the pieces not nesting into each other, and the mosaic will not hold well.
Weather you use this technique or another, it is a good idea to use a reproduction of your original. By doing so, you have a model to guide you. This is particularly useful if you gift the puzzle, and the recipient has never seen the original.
If you have a printer and are patient enough to cut traditional puzzle shapes from a blank model, there are a couple of great tools we found online. Have a look at this puzzle tool on Telegnom.org. There are also several templates on Twinkl, but unlike the previous one, you will need to create an account.
There are also retail options for blank puzzle pieces, and they vary greatly in price and quality. CreateJigsawPuzzle has a good selection, including wooden and acrylic pieces, beside the regular cardboard.
Pikkii sells blank puzzles with a traditional style painting frame printed along the edges.
If you buy blank puzzles to draw or paint on, take a photo of your drawing after it is done, so you have a guide when you put it back together.
Images that fill the page, and show a variety of colors and contrasts, make great puzzles.