Start by thoroughly washing and drying all your herbs*.
Scallions - most of the dark greens are removed along with the root. Remove any dry layers around the outside. Try to find younger, thinner, scallions instead of mature, thick ones.
Herbs - large stems should be removed, but should still be attached to tender stems if they are edible ones, like cilantro, parsley, basil, and mint. You shouldn't be placing just leaves on the platter, but tiny clusters of leaves connected with tender stems. For tarragon, you can leave slightly longer stems, but remove anything woody.
Radishes - stems and roots should be removed, with the exception being baby radishes fresh from the garden that have edible roots and stems.
Limes or Naranj - Cut into wedges for easy squeezing and snacking. You can cut the top and bottom of the lime off before wedging, but it isn't required.
Arrange all the items on a large platter so they are easy to tell each one apart from the others.
Notes
Sabzi Khordan is casual and rustic. However, there is a craft and care given to the preparation. Each item should be prepared as a reflection of its best self. The idea is that your guests shouldn't have to look at anything they grab off this plate, knowing that it's already prepared for enjoyment.* I wash my herbs one kind at a time and dry them using a salad spinner. This makes it easier to keep them separate for when I arrange them on the platter.