Your first parsnip harvest
Follow a starter plot from seed to harvest day.
Make a plot you can water
Hoe one tile per seed, plant the parsnips, then water the planted tiles. Keep the patch together so you can see any dry tile before leaving the farm. For seeds planted on Spring 1, the first expected harvest is Spring 5.
If one plant is behind
Check which tile you missed. A dry growing day delays that plant, so two seeds planted together can mature on different mornings. Harvest the ready ones and keep watering the rest. After harvesting a parsnip, you need another seed for the next crop.
Mechanics reference: Parsnip · Stardew Valley Wiki.