If you don’t want to buy a complete pumpkin carving kit, you can keep it simple and just invest in a mini hand-held saw instead. Keep in mind that saws with closer, smaller “teeth” will provide higher detail.
Hold the saw like a pencil, and keep it perpendicular to the pumpkin. Push it in and out of the pumpkin - the saw will cut its way through in its own. It’s best not to force it.
Make lots of little cuts rather than one big cut.
Start at the center of the design and work outwards. (Each time you remove a piece of the design, the pumpkin gets weaker.)