I agree that eating seasonally is the way to go! Right now, in addition to squash, that might include cabbage, kale, chard, brussels sprouts, cauliflower.
I personally like my veggies cooked, with a little butter or olive oil, and additions like garlic, nuts, bacon, herbs, or vinegar. My daughter mostly likes them raw. You'd be amazed what you can eat raw! She'll eat celery, carrots, bell pepper, peas, jicama, tomatoes, broccoli that way -- even green beans.
We also eat a lot of green salads. Sometimes she wants hers with dressing, and sometimes she just eats lettuce leaves.
A lot of kids like their vegetables with a dipping sauce, like ranch dressing (easy to make, you don't need to buy the bottles) or hummus.