Hi A.. I've been through this myself with my own kids, and with many of my students as well (I teach preschool and parenting). The biggest thing to remember is that little ones go through phases where the balance between what they want and what they are capable of doing gets out of whack. And the result is a really short fuse, tantrums.
As parents we need to remember that this too shall pass. And that they are not trying to be "bad", they are just struggling to figure life out. And getting overwhelmed. What we don't want is for your son to get "stuck" in this behavior pattern -- that is, acting out to get attention and not sure how to get his needs met in a positive way. So here are some suggestions to help with that.
So the first thing to do is catch him being good. Give him lots of positive attention when he is behaving well. With my 2 year old students I would greet them as soon as they came into the classroom, let them know how glad I was to see them. With my own kids, I would give them my attention when they first got up in the morning. And have some activity to do together right after breakfast. Then they were much more willing to play independently later in the morning (letting me get other things done).
The second thing is, to give some serious thought to your rules around the house. Put breakables away, make it a kid friendly environment -- so that you don't spend all day saying "no", "stop", and that sort of thing. This way, you can save the negative feedback for behaviors that really matter (hurting people). This is the time to pick your battles carefully -- and save your own sanity. Don't worry, as your son gets older you can impose greater limits and expectations as he is ready for them.
The next thing is, give some thought to how you respond to your son's negative behaviors. A lot of acting out at this age is either venting overwhelming emotions... or testing the boundaries. And no matter which your son is doing, it will help you both if you can appear calm and firm and loving. Remember, he's acting this way because his world feels out of his control. Things are not going the way he wants. And he doesn't know how to fix it. What a relief to feel that Mom does! Even if she limits his behavior.
When he is overwhelmed, offer sympathy and understanding. You can do this with a hug and with verbally stating what is going on, "You are angry that I won't let you eat cookies right now." Restate reality, "Cookies are yummy. But they are not good for you (or etc.)." Redirect, "But guess what? We can pick a yummy snack that is good for us." Offer a choice, "Would you like a rice cake or apple slices?"
Above all, make sure your son gets redirected to an appropriate activity -- rather than just saying "no". Very young children need our help in finding appropriate ways to express their feelings, energy, and creativity. They get stuck on an idea, and often need us to suggest a new one.
So for instance, when he tries to hit you, calmly tell him, "Stop. I don't like it when you hit me. Don't hit Mommy. You can hit that pillow over there. Here like this..." And encourage him to join in with hitting the pillow. You can even get silly and make a game of it. If everyone ends up laughing, so much the better.
But there will be times when he would prefer to rage and fume. In a calm and upbeat way, restate the problem and your limit. "You're mad." And restate what your son can do about it, "It's okay to cry about it if you need to. Let me know if you need a hug." And then get on about your business. Try to ignore the acting out. As a teacher I once knew said, "If need be, step over the tantrum." Let it blow over like a sudden storm. And be ready to give your son love and attention when he's done. This reassures him that while you don't like the behavior. You do love him.
Be consistent with this routine and the tantrums will become fewer and farther between. Just make sure you have a back up plan for what to do when it happens at the grocery store or a friends house.
The important thing is for him to learn that his feelings (anger, lonliness, etc.) are okay. And that he is okay for having them. BUT that hurting other people will not be allowed and that he won't get his way just by having a fit. AND there are other ways to let the feelings out that are just fine. Most of all, he is learning to trust you. To see you as a smart, loving guardian who has his best interests at heart. As you meet his needs for attention in a positive, proactive way -- and give him choices -- he will have less and less motivation to throw severe tantrums to get his way. You two can develop a relationship where you talk about why he can't have what he wants, where you negotiate safe alternatives, and where you work out solutions together.