There are few people who manage to agree on everything in life, and this is the reason compromise is an important facet of a good relationship. Major and minor issues may force a couple to learn how to compromise as the relationship gets started, and this is a normal part of life. It may be one wants orange walls and purple furniture, and the other person wants beige walls and green furniture. Compromising in a case like this will take good negotiation skills as well as the ability to find out the basis of each person's choices.
Learning how to compromise is not about giving in to a partner, it is about finding out why they need something different and finding a way to satisfy both people. Listening is a major component, and digging for the facts is also a factor. People generally have reasons for what they want, and taking the time to find out what drives their needs is generally a good place to begin finding a compromise both people can live with.