Step 1: Steady camera, long exposure, no flash
I used a Canon PowerShot A70 to take all the pumpkin pictures. It has some manual settings modes were you can adjust the exposure time and F-stops. I actually used the "Tv" setting which allows me to set the exposure time and the camera automatically adjusts the F-stop.
If your camera doesn't have any manual modes, turn the flash off and see if it can compensate enough. The answer is it probably isn't enough. If you're really into taking pictures of pumpkins, like me, make sure your next camera has a manual exposure mode (my other criteria was a water proof case...).
Step 2: Tripod or tripod-like thing
The mini tripods are ok and I keep one in my camera case for when I don't have my tripod.
If you're just setting the camera on something, use the delayed shutter function. With it, you can press the button, take your hand off the camera, and know it'll stop wiggling before the picture is taken.
Step 3: Background
Here, I just have the pumpkins sitting on the dining room table. Behind them is a wall with no windows. I should have removed that flower vase as you'll see in the external lighting step.