A garden bed isn't a requirement for growing potatoes. Fabric grow bags, five-gallon buckets, and even large plastic totes all work well, and the core technique, hilling, translates directly: it just means adding soil to a container instead of mounding a row.
Look for something at least 10-15 gallons in volume for a full-size harvest from a single seed potato, with drainage holes in the bottom being non-negotiable; potatoes left sitting in waterlogged soil rot quickly. Fabric grow bags are the most popular option because they breathe, which helps prevent overheating and keeps roots from circling the way they do in solid plastic. A five-gallon bucket works for one or two seed pieces but will produce a noticeably smaller yield than a proper grow bag.
Start with only 4-6 inches of soil in the bottom of the container. Set one or two seed pieces on top, eyes up, and cover with another 3-4 inches of soil. As the plant grows and reaches 6-8 inches above the soil line, add more soil or mulch, burying the lower stem and leaving only the top leaves exposed, exactly as you would with hilling in a garden bed. Repeat this as the plant grows, gradually filling the container toward the top over several weeks.
This staged filling matters because, as in a garden bed, tubers form along the buried stem above the original seed piece. Filling gradually rather than all at once maximizes the length of buried stem available for tubers to form on.
Use a light, well-draining potting mix rather than dense garden soil, which compacts in a container and restricts tuber development. A mix of potting soil with compost worked in gives both drainage and nutrients. Containers dry out faster than garden beds, especially fabric grow bags in full sun, so plan on checking moisture more frequently than you would for an in-ground planting.
Container soil loses moisture faster than garden soil, so watering needs are typically more frequent, often daily in hot weather. The same consistency principle from in-ground growing applies here, and arguably matters more: containers have less buffer soil moisture to fall back on, so a container that dries out completely and then gets soaked is an easy way to trigger hollow heart or cracked tubers.
Potatoes want at least six hours of direct sun daily. A patio or balcony spot that gets strong afternoon sun is ideal, though in very hot climates some afternoon shade can prevent the container itself from overheating and cooking the roots.
This is the easiest part of container growing. Once the foliage yellows and dies back, simply tip the container over onto a tarp and sift through the soil by hand, no digging required. For timing details on when to harvest for new potatoes versus full storage potatoes, see When and How to Harvest Potatoes.