there are varying ways in which firms employ research. what i am about to tell you is how my firm does so.
a design team is usually comprised of a human factors specialist (researcher), designers (ID, IaD, Graphic, etc…) and Engineer (ME, EE, ect) as seen fit for each project. For example my last project was a Human Factors person, a graphic designer, an ME and myself (an Industrial Designer).
The Human Factors person generally leads the research efforts but each member of the team is critical during the research phase as well.
So I guess you are wondering what I mean when I say research. This can be many things. But most often research is what you do to understand what is happening and why it happens or more relatively this means what people are doing and why they do it. There is alot of ethnography and psychology involved here with all parties of the research effort needing to have empathy for the people that they are observing.
There are many methods that researchers use to uncover this research. You can go to school to learn them, you can learn them on the job (as I have) or you can read about them in books… or you can try all three.
There are research firms that do this type of research in a quite detailed manner and then provide their clients with the data… I find this type of work to be the least helpful for actual design, because just dumping data on a table doesn’t really give you any direction as to how to solve problems.
The way my firm and a lot of other top tier firms approach design research is a bit different (and why i think it is best suited for successful design practices).
It’s less about every detail and more about having an eye or ear rather for the most important details. Taking these details/observations/patterns/stories and creating a context for understanding problems and principles that you can then go about solving these problems with.
This last part is often called synthesis. It is hard, and not alot of people are good at it. Clients will often ask how synthesis works and there is never a good answer for this question, because its a very organic process. But in the end good research is nothing without, intelligent synthesis and both are the backbone of design strategy. And from design strategy is born viable conceptualization.
You could write pages about design research (which people have, they are called theses, or books) but this is my quick after lunch summary.