The supplies should cost about $10 or less. You will need:
1x pumpkin (of course!)
1x Blue LED
Stiff wire (coat hanger, florist's wire, etc.) to maintain the growth's shape
Electrical wire (insulated or enameled) - at least a couple feet. Thinner wire will be easier to hide.
Battery holder (4x "AA" or "AAA" (etc.), or 9V battery snap) and batteries
Resistor (value depends on battery holder)
Hot-melt glue and gluegun
Step 1: Choose your battery holder and resistor
A resistor's "stopping power" or resistance is measured in Ohms; the higher this value, the more strongly it resists the flow of current. A typical blue LED can handle 20-30mA of current. For either type of battery holder, a resistor value in the range of 250 to 560 will work fine (you can use higher values to make the LED dimmer). If you are using a 4-cell holder, you can go as low as 100 ohms.
1/4 Watt is the most common size of resistor you will find, and will be fine for this project. You can use larger wattages (1/2W, etc.) if you have one lying around, but I wouldn't recommend going smaller. Since it's hard to inscribe a numeric value on the round package (and harder still to read!), resistors at this size are normally marked with colored bands to indicate the resistance. If you are faced with a package of assorted resistors without numeric values, look up "resistor color code" for help in identifying the correct one.