Having spent some time on this site and being a confidante to my friends, I find that many people have difficulties communicating. So let's talk about Communication in Relationships. 
5 Traits of Effective Communication in Relationships
1. Be willing to listen. Many times we 'listen' without actually listening. Many people half-listen and are busy forming their response as they listen, your partner deserves your full attention, listen to everything. They're telling you a lot through their words and their body language, their tone of voice, the words that they choose.
2. Show empathy. Pretend you are in their shoes, feeling those emotions, try to empathize with them. It will help you to understand their feelings and perhaps understand why they are feeling the way they do or why they did what they did.
3. Be kind. Don't attack the other person. You should never make personal attacks ('you're crazy', 'it's all your fault'), you are likely to put the other person on the defensive and that does not make for a constructive conversation.
4. Be prepared. Make sure you're calm, if you are angry, you are likely to not be kind. Try to find a good time to talk, one in which neither of you feels rushed, you have a quiet space, and it is private (or private enough to hold a conversation). Try to analyze your feelings first, what do you want to talk about, why does that issue bother you, know how much you are willing to compromise. If you go to someone and say, I have a problem but I don't know why it's a problem other than it makes me sad/angry/jealous, then it can be difficult to solve the problem. Be careful, this doesn't mean to make a decision before talking to him/her, do not judge and sentence the other person before they have a chance to defend themselves.
5. Be open, be willing to compromise. A relationship is a two way street, you can't communicate alone (communicating alone is talking AT someone) and you can't sustain a relationship alone. A relationship is about give and take. Compromise and come to a solution both parties can agree on. If you're not willing to compromise, it should be over a major issue and that's not communicating, that's issuing an ultimatum.
What should I communicate?
1. Major Life Situations/Decisions. This person is now a part of your life, your decisions affect him/her, changes in your life are also important to him/her. If you sustained a major injury, they would want to know. Consider it as, if you were in their shoes, would you probably want to know? And once you know them well enough, is this something they would want you to tell them?
2. Significant feelings. If there is something that he/she does or say that is making you unsatisfied or unhappy. Talk about it with him/her sooner rather than later. You don't want to build up resentment and you don't want to spend more time unsatisfied/unhappy. Or he/she did something that made you exceptionally happy or exceptionally proud, tell them. It makes them feel good, and it gives them feedback, it encourages them to do more of those actions or to do similar actions. You want to communicate the good and the bad.
In my opinion, these are all fairly simple tips and suggestions, but they are very effective. If I've missed anything you think is vital, please add it below. If there is anything you'd like me to elaborate on, please let me know.
Most Helpful Opinions