When you are designing a research experiment you want to first have your research question and your research hypothesis. What do you expect to find when you are looking at subjects managing interpersonal relationships of the romantic variety?
After you have done this you then want to look at what are the variables you are looking at and if you are looking for differences between or relationships within those variables. For example do you could look at the relationship within the variables of having more than two romantic relationships on Facebook and the ultimate success of those relationships or you could look at the differences between those who meet one person on Facebook and those who pursue several relationships on Facebook and the success of those relationships.
In regards to your methods, the statistical analysis you will run will be determined by the type of data that you have, how many variables you are working with, and what type of information you are seeking. For example if you are looking for causation you cannot use a t-test but would want to use a regression.