The flat of plugs you receive will be individual molded cells, all connected. They are each several inches deep, but not very wide at all (less than 2 inches across, I believe). The narrow deep cells are perfect for these milkweed seedlings, because they develop a taproot.
If you are planting just one flat, you can use a narrow trowel to dig the holes. If you have a bad back or want to save time planting multiple flats, then you might want to purchase a bulb auger bit for a cordless drill. It doesn’t need to be a big expensive one.
On planting day, squeeze the bottom of a cell gently to get the soil and roots loose from the sides of the pot, and then gently lift out the plant. Don’t take the plants out before their hole is dug. You want the roots to stay moist and away from air which can dry them quickly. Pop the little transplant into the hole, and fill with soil, making sure that the roots make good contact with the surrounding soil. Do not bury deeper than they were growing, planting them just at the level they came.
Water each transplant as soon as possible, and check to make sure there are no gaps where the soil settled when you watered. The number one killer of transplants is an air gap between the soil and the roots.
Transplants would probably benefit from one or two more waterings several days apart, but then should be self sustaining. They may sulk and wither after transplanting, but should regrow from the taproot. Don’t be discouraged if they take a nap during the heat of summer. They may sprout again in the fall, or wait until spring to regrow.