Think about other people that you know, and how they would react in a certain situation. Think about memories that you have of things that have happened to them, and how they have acted. Consider characters from movies and TV shows that you have watched, and jot down some notes on how they reacted to situations, and classify their personalities based on their separate characteristics. For example, how did person X react when person Y broke up with them? Were they understanding, explosive, devastated, etc. Why do you think they reacted the way they did? If they had a different personality, would they have reacted differently?
Also, perhaps you could visit a personality site such as www.16personalities.com. It might help you to understand the different personality types, and how they act or react in everyday life.
Another tip: Be consistent with personality types with your characters. If you want to create realistic characters, your readers should find themselves thinking "That sounds like something Joe would do/say." You do NOT want to have your characters do or say something that does not fit with how you have portrayed them elsewhere.
There are two steps here.
The first is ensuring that you have characters who do not think and act like you do. Since it's not happening automatically, you may need to actively assign characters traits that are unlike yours. When a new character is introduced, stop and think about it.
One thing that can help is trying to assign character types. It doesn't matter which ones. I have heard of people having success with Myers-Briggs character types, I have heard of people having success with the twelve Olympian gods. Pick a character type and run with it.
Which leads to the second, which is remembering what the character is supposed to be like under that type. Slow, conscious reflection on the matter may be the only way to start out. You can think of it as a writing exercise. You may even find it helpful to write unrelated short pieces, not full stories, simply to write about a character like that.
Read obscure texts. I'm currently writing a novel where I'm blatantly stealing a character from a novel written in 1800. I'm sure nobody has ever heard of the original character because this Chinese novel was never translated into English.
Ok, you don't have to go that obscure. But pick your favourite character from a book you really like. Just don't pick Harry Potter. Change enough details to make them unrecognisable.
When writing your story, really get into their heads. Remember that every character is the hero of his own story. Did you (the author) not give Mr. Sneed enough action last chapter, leaving him stuck in the office all week? Mr. Sneed is bitter about that. He's angry about his fate. After all, he's the true hero of this story!
Try to see the world from their POV.
When the "hero" captures Mr. Sneed and puts him behind bars, Mr. Sneed is filled with righteous indignation. Is there no justice in this world?
Everyone thinks that the "hero" is some sort of godsend... but only Mr. Sneed knows the truth.
People are sheep.
I normally just make characters that combine people I know, and other characters I've written before. For example, my character James in a book I'm writing seems to be a combination of a boy named Daniel I know, and a character named Obvious Lee from a musical I wrote call Reflected Magic.