Drill two to four 1/4-inch holes in the box’s bottom if it doesn't already contain drainage outlets. Use a plastic or wooden box that is 12 inches deep and at least 12 inches wide. Three- to 5-gallon containers work well.
Mix 2 to 3 tablespoons of an all-purpose, slow-release fertilizer with a soilless potting medium. Add just enough water to the medium moistening it evenly throughout and place it in the container.
Set the container in an area with at least six and preferably eight hours of direct sunlight. Insert a pot espalier into the soil supporting the plant, or set the pot against a fence or permanently affixed trellis supporting the butternut as it grows.
Sow two to three seeds in the box’s center, planting them 1 to 1-½ inches deep. Water the pot every one to two days, so that the soil remains moist. The seeds typically germinate and sprouts begin emerging in seven to 10 days.
Pinch the excess seedlings if all three seeds sprout, so that only one remains in the pot. Continue watering the soil as necessary.
Tie the butternut’s main stem to the espalier or trellis once it is at least 8 inches long or long enough to easily reach the support. Tie it loosely with a cloth plant tie.
Continue tying the vine to the trellis as the plant grows, spacing the ties every 6 to 8 inches. Tie cloth slings, made from old t-shirts or nylon hose to the trellis by each developing squash. Set the squash in the sling so it supports the vegetable as it grows.
Harvest the butternut squash when the rind begins hardening and after the color changes from green to a buttery-brown or orange color. Cut the ripe squash from the vine with a sharp knife.