Cut off ends of cucumbers, and peel strips from skins, leaving thin stripes of green still showing. (If you don't have European cucumbers and are using supermarket cucumbers with waxed skins, you may want to peel them completely.) Cut cucumbers into half lengthwise, then cut each half lengthwise into thirds, and slice. You should have bite-sized pieces not more than an inch wide. Place cucumbers into plastic bowl.
Wash and dry fresh dill, then remove the thin stems with delicate leaves from the thicker main stems. Discard thick main stems and finely chop thin stems and leaves. Add dill to the cucumbers and stir to combine. Add yogurt to cucumber-dill mixture, stirring to coat all pieces of cucumber with yogurt. Gently fold in feta, being careful not to over-mix. Season to taste with salt and fresh ground black pepper and serve immediately.