Misunderstandings are common and impossible to completely eliminate, but we can understand some of the things that go into misunderstanding someone or something and, in that much, make a bit of progress minimising them.
The challenge is you don't know when its happened. If you *don't understand* then you know this and you can ask for clarification. But if you misunderstand you actually think you have understood. The skill at hand then really comes down to how to be good at understanding things.
Preconceptions - you'd be mistaken to think you can really get around having them, but being aware of your preconceptions is the first step to being open to having them be shown wrong.
Double checking - Once you have your theory on what you've just heard or read, ask if you've understood correctly. Simple, but overall good practice.
Putting passion to the side - there's nothing worse for creating misunderstand than a person who eagerly jumps in because they hear a buzz word or they think they see an error. Passionate disagreement can be a good thing, but know it's time and place.
Know your weak spots - are you not very well read? Do you often equivocate words? Are you not good with subtlety? Can you not hold long arguments in mind? Have fun finding your weak spots. You'll have them. What's better, to know them or not know them?
What information don't you have? - this one is similar to preconceptions. Whatever argument, or whatever, you are facing has a context. It's solving a problem, it's a response to something, and so on. Be careful to keep track of this and know where you have a gap of information.
The skill of analysis - knowing how to analysis arguments is a great way to ensure you understand them. There are several things involved here. Comprehend the meaning of their language, discerning their meaning from other possible meanings. Prioritise the parts of their argument as they have. Gauge what kind of argument you've just gotten.