Growing vines from store bought yams and potatoes is relatively simple, it just takes time and patience. I've grown multiple vines from a variety of tubers. From the looks of it, you have sweet potatoes, not yams. Yams have rougher skin and are more cylindrical in shape. It is not unlikely for a sweet potato to be mislabeled, law or not. Plus, there are purple sweet potato varieties. Luckily, sweet potatoes are easy to grow!
A couple notes to start:
- You do have tubers. A tuber just means the swollen part of a plant's root system (the potato or yam), which holds the nutrients for the plant's growth.
- The growing process for a yam and a sweet potato are the same (or, very similar), because they're both tubers. So even if I'm wrong about your tubers, the same process should still work.
- Fun fact, they are not related. Sweet Potatoes are in the Morning Glory family, and Yams are in the Lily family. Also, potatoes are in the Nightshade family... don't eat any berries that grow on potato plants!
Most of your tubers will grow roots eventually, but you can start with the one pictures that already has a root or two. I've had more success not cutting pieces from my tubers, even though a lot of sites recommend that (mine rot quicker when cut, so the plant doesn't get the nutrients it needs). Here's some steps to take now:
- Place the tuber in a sunny spot, suspended with the root end in water. (Take a large jar and fill it part way with water. Stab some toothpicks in the upper end of the tuber, so they support it on the rim of the jar, while letting the bottom end sit in the water.)
- Let it grow! You'll see more roots grow, as well as "slips" on the top. The "slips" are the vine portion of the plant. They'll look like roots to start, but will grow upwards, and develop leaves.
- Once it has 2-3 slips (or more, or less, it's not hugely important), bury the tuber in a well draining pot with fresh potting soil, and keep the soil moist (don't soak it, or the tuber has a higher chance of rotting). I water mine about 1x per week, but that may vary.
- I find my sweet potato vines grow very quickly. You can let the vines grow indefinitely, or, for a fuller plant, cut the vines occasionally so it grows more shoots instead of longer shoots. (You can put cuttings in water to root them!)