To start, from what I have found only some plants can become their giant versions which include the tomato, pumpkin, and cucumber.

Growing the giant plants depends on which of the three you are going for. A giant tomato is grown by planting tomatoes in a 2x2 pattern which can be done on a 2x2 plot or larger. A giant pumpkin is grown with a 3x3 pattern, and a giant cucumber with a 2x2 pattern. Regardless of which plant you are attempting, watering robots should be placed close by.

It seems pretty random for when plants turn giant so I'd just recommend just planting your stuff like normal and hope to get lucky.

Harvesting a giant plant is done by clicking on it multiple times which will yield differently based on which of the three you are harvesting. Generally I've found them to be around double to quadruple your original seeds planted.

If you need the achievements, the best way to get them is to plant the crops far away from your harvesting robots and set your helpers harvesting priority to the lowest.

Hope this guide helps in your giant crop endeavors :)

Possible gold pumpkin variant however I have not grown one yet :(