Making Bismuth Crystals
To make bismuth crystals, start by melting the metal by heating from below until the cup and metal are well above the melting point (it melts very quickly in a propane flame). Then leave it to sit for a minute or more, depending on how hot you made it. You want to leave it alone, no shaking, no poking, while it's cooling, because any disturbance will start new crystals and you want to have just a few big one, not lots of small ones.
You want to wait until it's about 50% solid, and of course it will solidify from the outside in, leaving a molten pool in the middle. How can you tell when it's reached this point without disturbing it? You can't, so either guess, or blow lightly on it and watch how much of it wiggles. You can re-melt it as many times as it takes to get lucky, so don't worry if you guess wrong the first few times.
The video for this sample starts when it's reached this 50% solid stage: You see me pick it up (with a glove) and pour the liquid center off into another cup, then immediately zooms in to show the crystals I got. (The cut in the video is because it took several annoying seconds before the auto-focus settled.)
That's all there is to it. It took about half a dozen tries to get one I liked for this video.
Getting the much bigger crystals you see in, for example, the egg sample above probably requires higher purity metal, careful exclusion of unwanted seeds, and more careful control of the cooling time. As a general rule, slower cooling gives bigger crystals, but I really don't know the details for making big bismuth crystals in particular. I'm sure half a day's practice would do wonders for my results, but that's for another decade.