To start farming Grumpkins, you have to be at least level 8 Farming. You can find what your level is here:

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If you're not there yet, keep going!

Once you've fit Level 8, head to Buck's Galore in Terra Villa Central. Chat with Hazel and buy some seeds!

Once you've secured the seeds, head to a farm to begin planting. Grumpkins need to be watered twice: once when you've first planted, and again at the 90min mark. Don't forget, or you'll come back to dead crops! They'll be ripe and ready to harvest after 3 hours.