Good comunication is the answer to resolving conflicts and light everyday relationship issues. By "good" I mean "deep" :) Feel your partner, express your feelings, talk, make love, walk together, cook together, watch films, read books and respect his right to spend some time on his own without asking questions about it. Good luck!
The first step is to stop always trying to prove you are right and forcing the other person to agree with you. Decide that you can disagree on some things without destroying your relationship. Talk to each other, calmly and quietly. Explain your side of the problem in a few words, then listen to the other person do the same. See if the problem is really covering up a deeper, under-lying issue.
Resolving conflicts and common relationship issues is not always an easy know-how type of thing, but the basics are fairly simple. Find the biggest problem and start there. Are you communicating well? Is one giving more into the relationship than the other? Do you have regular set times to talk and work things out? Take the time to talk things through and really listen to one another. Put the other person first and your own needs and desires. Try to meet his or her needs before your own. This will help you to go down a path toward resolution.