Wash the squash then grate them on a box grater. You should end up with about 3 cups of grated squash. Grate the onion as well. Place the grated squash and onion in a mesh strainer and press to squeeze out some of the water.
Place the squash and onion in a large bowl, then add the flour, egg, sugar, and salt and mix until combined. Allow the mixture to sit for about 5 minutes.
Place a large skillet over medium-high heat and add enough oil to barely cover the bottom. Once the oil is hot, carefully place dollops (about 1 heaping tablespoon) of the batter into the skillet. Cook for 3 to 4 minutes or until golden brown. Carefully flip the fritters over and gently press them flat with the back side of a spatula. Cook another 3 to 4 minutes or until golden brown. Cook in batches, adding more oil if necessary, until all of the batter had been used. Drain on paper towels and eat immediately.
For a different flavor, add about 1/2 teaspoon of curry powder to the batter when mixing it up.
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