>>2747339>Tools.All you need is a knife and a saw. I use a Victorinox Ranger which has both, and more importantly, a locking blade. When I got home I used a hook knife (picrel) and sand paper to finish it off properly as I don't like carrying too much stuff with me.
>Wood.You can find wood when you're out. Hardwood is better. As for size, depends on what size spoon you're making. I like to work with dead/dry wood but some people find it easier to carve green/live wood. So yes, you can cut branches or logs and use those.
>Finished product.While I was out the spoon looked like a spoon but it was still rough and had jagged edges and loose bits on it. I took it home and finished it off properly, finally treating it with wood oil.
Try it out and see what works for you. I have friends who learned how to carve spoons at home before they tried it /out/. I prefer to keep busy in the woods, so I learned in the woods.