There are several methodologies for studying individual and group perceptions; it just depends on what your research questions are. If you're interested in learning about group perceptions about a topic in general, then a survey would likely suffice. If you're more focused on the intersection of perceptions, then a focus group is probably going to be more helpful.
You first need to map what perception(s) you're interested in examining, which population(s) you are interested in studying, and what relationships (if any) you want to explore in doing so.
I'm happy to give a specific recommendation if you can provide more detail on the research questions or the context and perceptions you're interested in studying.
I agree the approach will vary depending upon your question and how much is already known about the social phenomenon. If the key concepts are known already, a survey can be used. If there are mostly unknowns, a qualitative study using ethnography would be a good approach.