A Maremma puppy is ready for obedience training once it hits four to six months of age. This may seem early, but the breed has an above average intelligence level. It also has a tendency to make up its own mind, which means that obedience training is a must with this dog. Even after you get it into training, you will notice that the dog doesn't immediately obey your command. They will take a few minutes to think it over and decide whether what you are requesting sounds like a good idea to them. This reasoning ability is what makes them very good livestock guardians, but it is also what makes them less of a star in formal obedience trials. They just are not submissive dogs and really think that they have the last word, no matter what command you give them.
The dog's intelligence does work well for it in learning all of the commands. It can quickly master commands like heel and sit. This same willingness to learn can be seen in housetraining the dog. It is easily housetrained, even though most Maremmas are outside dogs. The obedience training that you give this dog should challenge this level of intelligence so it doesn't become quickly bored. A bored Maremma is an unresponsive Maremma.
You can't force a Maremma to do anything. It is typically not an eager to please dog either. So, if you find yourself being frustrated be careful that you don't try to punish or humiliate the dog to get it to do what you want. The dog won't forget your mistreatment and it will become very difficult to handle. It might even bite you if it thinks you are being treating it in an abusive manner.
One of the things that really help the dog to be more willing to obey is increasing its socialization. It needs to develop a bond with you, the handler, and your family. The dog is very affectionate once it is properly socialized, otherwise, it may not be as engaged or easy to train. It really excels at any activity that allows it to display its natural guardian instincts. You can let it guard your children, as long as it isn't guarding them against other children. The dog needs to be heavily socialized so that it can discriminate between someone who is visiting your home and someone who is invading your property line. It might not take your cue to heel if its guardian instincts take hold. Remember also, that if it thinks one of its charges is in danger it will make up its own mind on whether to protect against a perceived threat or not.