you can do it with just a knife but it's more difficult
to carve a nice regular depression in the spoon a gouge is very handful and i'd opt for a short and very sharp cutter for the rest.
Always use very very sharp tools. They will produce a better result and actually decrease the chance of cutting yourself.
Try to make many small superficial flakes instead of driving the blade deep into the wood
Wood choice is also very important. Try to find the best in your area.
Some wood will rise a small splinter instead of a nice controlled chip and it will be difficult to model small details.
If you make spoon also remember some woods are poisonus
(dont use yew for instance...)