From Ground: Start by watering the giant ragweed plant to ensure the soil around roots is damp. Once damp, dig a wide and deep trench around it with either a shovel or garden spade. The goal is to keep the root ball intact, so make sure to dig deep enough that you can get under it. Use the garden trowel for a finer touch near the roots to prevent unnecessary damage. Once free, place the plant onto a wheelbarrow or a plastic bag to transport it, being careful not to damage the root ball.
From Pot: If your giant ragweed plant is in a pot, start by watering it. Then, turn the pot sideways while gently tugging the plant by its base. The purpose is to slide the plant out along with its soil, keeping root disruption to a minimum. If it's hard to remove, run a knife or trowel around the edge of the pot to help loosen the soil and roots.
From Seedling Tray: Water the tray first, then gently hold the giant ragweed seedling by its leaves, not the stem, and use a dibber or pencil to push up the seedling from below. Always handle seedlings by their leaves to avoid damaging the fragile stem.