I am the mom of 3 kids, a 13 yr old boy, a 5 yr old boy, and a 4 month old girl. I can offer a few suggestions that helped with my kids.
First let me say each kid is different, so you'll need to find a way that works best for him. What I did with my kids worked like a charm and although they had a few tantrums in the beginning, I found that the way I handled it worked so well they stopped almost immediately.
Ok so using your situation as an example... I first would say something like "Silly boy you can't eat your breakfast down there, did you need some help?" (I would say this using a slightly goofy voice) DON'T make a huge deal about the tantrum and don't let him sense that it stresses you. Then I would say something like, "Here let me help you up so WE can take a deep breath and try to tell mommy what is wrong" Get down to his level, like on your knees, take a deep breath together - show him how. If you understand him enough to figure out what he wants/needs than that is helpful, if not what I would do is say "Look at this Yummy breakfast!" Depending on what it is, put some on a fork or spoon and say "Wow this bite looks delicious! Don't anyone take this bite when I'm not looking" Hold it low enough for him to steal it, and look away. When he steals it from you, Pretend to go to eat that bite and then realize it's gone and say "Hey who took my bite!?" (again being a bit goofy) You may have to do a couple times, then maybe say "nobody better eat this whole plate, while I'm not looking" Now this may not always work, but somethings to try are getting down to his level and speaking to him like a little person rather than a baby, making him laugh, or getting him interested in something else.
IN a store situation, like for example for a toy he wants, I would tell him, "oh wow, that's a cool toy, we will have to put that on our birthday/christmas list. But I'm sorry right now we can't get that because mommy only has enough money to buy what we need. Do you think you could help me find the things on my list?" If that tantrum continues, quickly try to revert his attention elsewhere, or say "ok now, mommy said not today" and walk away, but being sure to ALWAYS keep him in your sight!! He will most likely run after you. If he rides in the carriage, try to revert his attention and perhaps even try to make him laugh as you get away from that area. (laughter is amazing) Let him know that he has to listen to you no matter where you are. Always remember NEVER let him see that it stresses you.
Now there will be times that these methods just won't work. AT that point what I did was tell them if their tantrum continued they would get a time out. My time outs always were as long as they were old. And sometimes yes, they will cry it out. After the time out is up go back to them and get back down to his level and say to him as you probably wipe his tears, "Ok time out is over, do you know why mommy put you in time out?" See if he answers, and explain to him what his bad behavior was, why it was bad... example "When you throw your tantrums, I can't understand what you need or want" AND then offer other ways he can handle it like "The next time you feel like you are getting upset, you tell mommy ok? That way I can know what you want or need, and we'll take a deep breath together, ok?" Give him a big hug and kiss and say "That's my big boy!" and tell him you love him.
Basically he is at the age where he is trying to see where he stands... He is trying to communicate but is probably getting frustrated with trying to convey what he feels or wants. Try to explain things to him as per his age and treat him like a little person and also show him lots of love and understanding. ALthough sometimes it is needed to be stern.
I see that you are a full time employee, I am a stay at home mom, but I DO NOT believe it has anything to do with how much you work. I worked full time when my oldest was little and he went to preschool since he was 3. I worked long hours back then as we needed the money. He was in preschool all day. One thing I did notice is that he would watch how the other kids acted with their parents and sometimes come home and try it out with us. Sometimes they will pick up the habits of other kids. That you will need to nip in the bud. Be stern and tell him that isn't how we act like a big boy. But again try to find something that you know will work with your child. It's all about how you handle him when you are there and the quality of the time together.
I always found that laughter or distraction helped to diffuse my situations. But there were times where I had to be stern. You have to not only find something that will work with your child but also you need to teach them that you & your husband/boyfriend/ect are the bosses. Also try giving him little duties around the house like dusting, sweeping or mopping and then praising him for doing so. (don't worry if it's not a great job) this will not only teach him resposibility but also that he is an important part of the family and he will most likely feel special to have a special job around the house and make him feel more like a big boy. And make sure you praise him and tell him what a great job he did, or how proud you are of him for how he handled a situation ect. If he does really good then maybe do a special activity or craft or whatever with him always telling him how proud of him your are.
I hope I offered at least a few ideas for you. I am hoping this works with my new little daughter! I plan on doing the same with her. Good luck!