I have a 27 month (2 year +) old daughter and she is a handful. Hence, my opinion in this post is not based on hearsay or from other parenting blogs, but from our experiences with our daughter. And like most learning, these have also majorly come from failing to communicate in the first place.
1. Kids don't understand sarcasm
2 year old kids are at the very nascent stages of communication learning curve. They don't understand complex of figure of speech like sarcasm or rhetorical questions. I'm sure every parent is aware but this point gets missed in the heat of the moment. So when your kid has just emptied an entire glass full of juice on your couch and you should 'neat! that should make you happy. no?'. They don't know what you mean! You are only spending your intellect on something totally uncalled for.
2. They are allowed to shout; you are not.
It's not a parliament where you will win (or assume to have won) an argument by shouting on top of each other's voice. Kids will always win this. Shouting and screaming is a way of expression for the kids. They feel something and don't know how to express it. I hope that is not the case with most adults reading this. Hence, they are allowed shouting while you are not. :)
3. Create diversions
Kids easily get diverted. So keep diversions like music, books, toys, videos, pictures, crayons handy. Picking up a crying toddler and taking them to the balcony to show a street dog or a buffalo is an old trick in the book that we all tend to forget.
As a parent, your priorities will change. I'm sure you know that. But not in the long run like outings, late night parties, watching TV/ movies etc. but also at every instance. You may have to choose discipline over peace of mind, entertainment over cleanliness etc. Imagine you have invited guests over for dinner and your toddler decides that it is THE day to cling on to her favourite parent. "Why did she chose today? She does this on purpose! She wants to embarrass me" - You are bound to be irritated because you see a potential personal embarrassment! You are afraid the guests will have to face a half hearted welcome. But guess what? You haven't prioritized well. Which results in you shouting back at your kid instead of making the arrival of guests equally exciting for her.
5. Ask or walk away
When kids start crying unnecessarily (or so you think), don't tell them to stop crying as an immediate reaction. We all get irritated when a kid is crying in the vicinity. But research shows that is the intent of crying. Humans are programmed to be disturbed by a crying child so that the child's needs can be catered to. So, when your toddler begins to cry, ask her WHY she is crying? If you cannot hear her properly, tell her that you cannot make out what she wants to say because she is crying. If there is a genuine reason, address it or refer point 3 above :). If there is no reason the kid can give, it could be hunger, internal pain or discomfort that she has not experienced before etc. If it looks like a tantrum and diversion doesn't work, walk away. Just tell the kid that you are willing to talk once she has stopped crying. You may have to bear with the crying for a few minutes, but you would have made a point.
There are many more aspects to communicating with a child. I hope as I learn from my experiences, I am able to articulate them for the readers.