The scientific method applies to hard and soft sciences alike, chemistry and political science both. In this method, which is the basis for all scientific knowledge, you attempt to answer a research question. To use our very elementary example: What happens to water when the temperature changes? Based on your knowledge and experience, you have a well-educated guess: When the temperature rises above 202 degrees Fahrenheit, the water will evaporate into gas; when it dips below 32 degrees Fahrenheit, the water will freeze into solid ice. This is your hypothesis. Your experiment will test your hypothesis, and your observations during the experiment will form the basis of your conclusions.
The dependent variable is what is measured in the experiment. In our example, the dependent variable is water. In a more complex example, let's say you wanted to test the relationship between religiosity and support for same-sex marriage among individuals. In this case, support for same-sex marriage would be the dependent variable, as it is the variable being affected by the degree of an individual's religious faith.
The independent variable, then, is the variable that affects the dependent variable. In a hard-science setting, it is the variable you, the experimenter, control; you alter the temperature to study its effect on the liquid water. In the social sciences, it is the variable you study to see how it impacts your dependent variable. So, then, you would study religiosity, perhaps measured by the frequency of religious service attendance, to see how it impacts one's support for same-sex marriage.
The hypothesis is the basis for the experiment; your best guess of how the independent variable will affect the dependent variable. You could hypothesize that, based on your prior research, in individuals, higher levels of religiosity will correlate with lower levels of support for same-sex marriage, or that decreasing the temperature of water below 32 degrees Fahrenheit will cause the liquid to freeze into solid ice. You can then test these hypotheses, either through advanced statistical analysis or laboratory observation, and participate in humanity's expansion of knowledge.