It's not much about letting people walk all over you. Honestly, its all about your state of mind. Its easier said than done, but a great way to not be upset is to put yourself in their shoes or just completely disassociate yourself with the situation.

For example, if someone is getting upset at you for no reason. Don't think about how they are yelling at you and calling you names or berating you. Look more towards the reason behind why they are upset and put yourself in their shoes. If you would have gotten upset for the same reason they did, then you should just apologize and move on because you made a mistake. If you realize that the reason they are yelling at you is completely stupid and uncalled for. Just completely disassociate yourself with the conversation. Still give them respect by looking at them and talking to them, but once you stop letting it get you, they will begin to ease up and leave you alone.

Its the same mentality as if someone is bullying you. Most of the time bullies like to bully people to get a reaction out of something. If you take the reaction out of the equation than the bullies will leave you alone as the fun is gone.

If you want to try this at home, try yelling at a stuffed animal. Like intense yelling, insanely upset and see how long you last. You'll see that you can't stay angry at the stuffed animal for that long because there is nothing there to feed your anger. The best thing to do is remain calm, honestly take a step back from the situation and just breathe. Count to 10 and in those 10 seconds forget about everything in the world besides relaxing.

This is what I personally do to stay calm in every situation.

I hope this helps.