Learning good communication skills and appropriate boundaries can help avoid big blow ups
I remember when I was first married at the ripe old age of 21 having the confidence that we could handle anything because we'd survived alot already. And while that was somewhat true, we were still vastly unprepared for how to resolve conflicts. Our premarital counseling just instructed us to "talk about it" and a few other super (sarcasm) helpful sayings like "don't let the sun go down on your anger". Which might have been great advice for some people, but not for us.
We had to learn along the way what the edges were. In my work with couples in session, this is typically one of the first things we cover because it's foundational to the health of the relationship! Hopefully you are spared the harm that comes from learning the hard way!
No Name Calling. trust me on this, you will spend more time fighting about what you said, than about their/your legitimate complaint and the conflict will drag on for way too long. Don't call names, don't even call them "childish" or say they are "acting like a" insert thing here. It's a lose-lose.
Speak For Yourself. This one is two-fold.
Using I-statements and sharing from your own experience are more likely to be received positively as problem solving attempts instead of character attacks. "I feel far away from you when you are on your phone while we are spending time together" is different than "You're always on your phone/ You never pay attention to me".
Don't read their mind and don't expect them to read yours. Even if they're really good at it or you are really transparent. Just don't. Somewhere, some one will be disappointed by this.
Use Inside Voices. I can easily recall conversations at an inside voice level. When the other person starts yelling, I check out. Learned there's a reason for this, and it's experienced almost universally. Being yelled at triggers our Flight or Fight response because it should be used for danger or emergencies only. If you're yelling, chances are high that you're breaking the other rules as well, and it's time for a break.
Make time to hear each other out. Your first task is to listen to them, and then to be heard. It's fundamental to getting conflict resolved and finding solutions. In our house, we have to schedule a time, usually after the kids are in bed, so we are in a good place when it comes.
Leave others out of it. Don't bring up the other person's parenting, job, family of origin, or any other outsiders unless that's the topic. Approaching your partner about the way they discipline is much different than "piling on" during a conflict about who's going to pay the vet bill. Stick to the task at hand, and focus on one problem at a time!
Take it up with them. If you have a problem or disagreement with your partner, parent, or friend, express your feelings directly, and appropriately (like, probably don't cuss them out on facebook) with the person responsible. Venting is definitely OK. Just make it clear you are venting to them and not about them.
That's the list my friends. Each relationship might have additional "rules" specific to you or your partner's needs. And I'm confident you will find more as you work with these. Learning the boundaries of you and your partner is one of the hardest challenges of early coupling. Stick with it, and you'll be experts in a matter of weeks.