The age at which a baby begins feeding himself very much depends on his parents' attitude. Many 1 year old babies are already familiar and accept getting fed with the spoon.
On the other hand, there are babies whose parents are so extremely protective that at any given time they are ready to say their bundle of joys are not ready yet to feed by themselves.
The moment in which the baby learns to feed himself very much depends on the chance given by his parents. Many babies are capable to manuveur the spoon on their own when they get to 9-12 months old. If permitted, by 15 months old, they learn to feed themselves without any help. Actually, a baby starts to prepare maneuvering the spoon as early as 6 months old, when he wants to hold in his hand the spoon or the food that's given to him. When they reach 9 months, most of the babies want to first grab onto the small pieces of food, then stick them in their mouths.
A more 'polite' baby' could simply rest his arm or softly touch the parent's hand when he is getting fed, but most babies, they will try to grab the spoon from the parent's hand when they feel they are ready for it. If your little one tries to grab the spoon out of your hand, let him have is and have another spoon ready as a backup. Even if your baby doesn't do it for fun, he will soon enough realize that feeding himself is more complicated than just grabbing the spoon.
It it possible for a few weeks to go by until he will learn how to get the food with the spoon, and a few more weeks to realize he shouldn't twist it sideways because he will lose the food. Most babies, until they learn to feed themselves with the spoon, will make a total mess on themselves and their surroundings. This happens because the babies get bored and tired of trying to grab the food with the spoon and not drop it until it reaches their mouths. So they become aggitated and throw and mix the food. This is when the parent should take the food away and only leave a few pieces of food behind so that they baby can still practice.
Stimultate the baby's curiousity, with colorful plates, bowls, and spoons, as well as with diverse tastes and flavors in the food they eat.