Mark out a 4-foot-square area in the vegetable garden, using a tape measure and can of spray paint.
Dig an 18-inch-deep hole at each corner of the marked square, using a post-hole digger.
Insert the bottom end of each of four 8- to 10-foot posts into the holes. Use 1- to 2-inch-diameter bamboo or 2-by-2-inch stock lumber.
Backfill each hole partway, using the dirt you removed when digging with the post-hole digger.
Bend each post toward the center of the 4-foot square area, aiming their tops so they meet in the center of the square.
Position the stepladder between two of the posts. Climb the ladder and push the ends of all four posts together. Secure them together in a teepee shape by wrapping twine around them about 4 to 6 inches from the ends. Wrap the twine around and around, forming a secure sleeve of twine. Tie off the end of twine and tuck in the loose end.
Backfill the post holes completely, firming the soil down gently but firmly with your foot.
Wrap twine around the entire structure, beginning at the bottom and spiraling the twine up as you go around, from the bottom to the top. Leave about 4 to 6 inches of vertical space between each wrap of twine. The twine creates a trellis that the pea vines can climb.
Sow a double row of pea seeds in early spring, spacing the seeds 2 inches apart in all directions around the perimeter of the structure, but not near any of the posts. Plant pea seeds only beneath the twine between the posts. Do not thin the pea vines. Encourage the vines to begin climbing upon the lowest round of twine by catching one of their leaves or tendrils on the twine. After that, they will continue climbing by themselves.
Plant eight to 10 bean seeds at the base of each post about two weeks before the average date of your last spring frost. Thin them to the four strongest seedlings when they are 3 to 4 inches high. Help them get started wrapping themselves around the posts when they are long enough to do so. Once they begin twining around the posts, they need no further help from you.