There are two basic approaches to quantitative research: experiments and surveys. For an experiment, you would need at a minimum a control group and an experimental group that received some kind of intervention, as well as a dependent variable to measure differences between the two groups.
For a survey, you would need to demonstrate how an independent variable affects a dependent variable in a sample that is large enough to detect such an effect.
David L Morgan thank you for enlightening us with your expertise. Could you please suggest what should be "large enough" sample? Is there any specific guidelines about sample selection?
Yes you can! However, your research questions and objectives will determine what kind of quantitative approach is more appropriate. As of sample size, you should not only be concerned about the number, but also how is it representative since you might attempt to generalize.