The scientific method of sociology is really no different from the scientific method of the “hard sciences.” The scientific method is simply a way of trying to determine what is true or not true through a systematic set of steps. In other words, it is a way of making sure that sociologists (in this case) are truly making legitimate discoveries about their fields of study.
In sociology, researchers start by forming a hypothesis. A sociologist looks at an area that is of interest to them and they ask questions about how certain aspects of that area come to be as they are. They form hypotheses that make predictions about these causes and effects. For example, a sociologist may wonder why girls get better grades in school than boys do (on average). They may then hypothesize that it might be because of peer pressure, family pressure, better relations with teachers, and other factors that they would lay out.
The researcher would then go on to test these hypotheses. They would try to find various types of evidence that could tell them which of the factors mentioned above are actually responsible for the result that they find. Because they are engaging in a scientific study, they need to look closely at their evidence and be sure that it really shows what they think it shows. They need to be careful not to let their personal feelings or opinions influence the conclusions they draw.
This is the scientific method in sociology. It consists of forming hypotheses and then objectively analyzing data to determine if those hypotheses are borne out by the evidence.