As trev said above, squash/pumpkins are very cold-sensitive plants. They generally only live one season. They can be easily grown from either seeds or transplants. Because of their temperature sensitivity, depending on where you live, you should wait until the soil warms up in mid-to-late spring. A soil temp of at least 60 - 65 degrees F is required. You can either direct-sow them into warm soil, or start them indoors in a warm medium and move them out when the soil has reached the minimum temps. Because yours was a volunteer, and doubtfully an heirloom, don't save the seeds from this year's pumpkin for planting. Eat them instead. They are nutritious and delicious both raw and cooked. Buy either seeds or transplants next season.

Pumpkins and squash are very easy to grow. Children often enjoy watching the seeds sprout and the plant begin to grow. If they are the only type of plant you want, then you could just start with a very small spot in your yard. However, as you've seen, they will spread quite prolifically. One vine could easily take over a small yard lol. Depending on where you live, they do suffer from a few pests and diseases. Put a few plants in so that if one fails, hopefully another will survive. If your determination is high, then research potential issues in your area and find preventative actions.

If you are looking for a better harvest, or just a healthy vine with the potential for a better harvest, they can be heavy feeders and usually enjoy a very rich soil. For a very cheap price, you can get a bag of composted manure and work that 8" - 16" down into your planting spot. Make sure it is 'composted'. Additional fertilizer may help, but for a fun project like you describe, a good manure should do fine. Let the soil 'mound-up' from mixing in the manure. Depending on the soil health, a spot that is approx. 16" - 18" across can support about 3 plants.

These plants love sunlight. Find the sunniest place that you are willing to devote. They also appreciate good watering. When they are very young, keep the soil moist so the seedlings don't dry out, but as they become young plants, and especially while they are getting established, try not to water everyday. They like evenly (over time) moist soil, but water very deeply, then wait until the top few inched are dry before you water again. Let rain work with you, and do not over-water. Many gardeners find that deep watering once a week works out fairly well. different soil types respond to water differently, so just pay attention and you'll do fine.

So, basically, if you provide a fertile soil, a sunny location, water well, and give them room, both pumpkins and winter squashes are some of the best plants to begin growing. There are literally thousands of varieties of differing shapes, uses, colors, and sizes. They are also some of the tastiest, and most nutritious fruits you can grow. Good luck, and have fun!