"How can I learn to do research?"
I would suggest that the only way to to develop research skills is by doing research, and reading the research of others.
I think of research as comprising the following steps...
1) What question do you want to answer? The more clearly the question is defined, the better.
2) Has the question already been answered? In the internet age, answering this question is much easier than before! Google and (for academic economics research) Econlit are the best ways to find out. You can access Econlit through the university library online.
3) Next, assuming the question has not already been answered adequately, you need to try to answer it yourself. Depending on the nature of the question, that may involve mathematical modelling (especially if you were doing a PhD or MPhil or other academic research), or statistical modelling. For the latter, you would need to find the appropriate data. There are many different sources of data; often experience is required to know where to look. As a starting point, see where related studies obtained their data. (Academic research should always clearly outline datasources; more popular research may not). There are some references on the Econ1002 course homepage of some sources of data- although they are just the tip of the iceberg.
This third step requires you to have or learn the appropriate tools in order to answer your question. For an undergraduate student, most questions you would be able to answer will be statistical in nature. A good understanding of statistics and econometrics is essential; you should be selecting your courses appropriately. If you have the ability and desire to go on to postgraduate studies, you should also be taking some difficult math courses, since these would give you an excellent foundation for later research work based on mathematical models.
4) Market your results. For academics, this is perhaps the most important step! More generally, if your research results are interesting and add to the stock of knowledge of how the world works, then you will want to pass on your results are widely as possible.
Here's a link on how to do research, although it's geared at postgrad Econ students....