Don't try to qualify people.
Do not let others feel contempt.
Don't speak any words outside what someone would commonly be able to accept.
Suppression of ego so others are not uncomfortable. Knowing when to not suppress it if others think you are fake.
Empathy implies you can feel with others. Example: You are a man and you talk to a woman. Being empathic means you have a clear mental image of what it might feel like to be a woman and can thus avoid saying things that aren't funny, like sexist bullshit. Or you talk to a student/junior and remember what it felt like when you had no fucking clue and how shitty it was when the old greybeards would scoff at you, with empathy you can talk to people where they are instead of highlighting the difference between you and them.
Most communicative problems I have ever seen (aside from language barriers) could have been resolved by a little bit of empathy.
Empathy is usually an internal process. On it's own, it wont't resolve a communication problem.
What ends up affecting a communication problem are the external actions that we take based on our internal empathy calculus (assuming we haven't totally miscalculated). Those actions will vary significantly by person and context, assuming any action follows at all.
Empathy is the relatively easy part. Acting on that empathy in a way that doesn't come across as condescending, disengaged, presumptious, judgemental, awkward, or scripted, while also remaining true to yourself and upholding your personal values are the hard parts.