How can a prospective PhD student know beforehand which universities have the most reputable teams/supervisors?
Most active does not mean most impactful or most influential. Reading papers on your own, you will have a hard time distinguishing good papers from mediocre work. Your best bet is to get recommendations from people who already work in that field. Ask professors at your own university for recommendations or opinions.
If you have a specific problem you are interested in working on, then it does make sense to search for papers on that problem and do your own reading. But you will still want to get advice from one or more people at your own institution who work in that area (or close to it).
Other answers suggested asking professors or asking students. I suggest you:
- Figure out what you want to do after your PhD, as specifically as possible
- Find people who are doing that
- Ask them who would be a good supervisor for your PhD
This strategy will get you the answer most customised to your needs.
Several of the answers suggest using Google Scholar or similar. Google Scholar will tell you which supervisors are producing nothing, but it will not tell you the difference between supervisors who publish a small amount of good work and those who do a lot of poor work but effectively manipulate the citation statistics.
Google Scholar and Research Gate are two general resources for finding a researcher's impact in their field. ArXiV also can provide some general information on who is recently publishing in the field. Individual/group websites can also provide some input as to the overall reputability of the professors in question.
I would consider compiling a small collection of universities you are most interested in on the whole, then researching the professors at those institutions. While university reputation is not an exact indicator of individual output and impact, the two topics are on the whole correlated. It is relatively likely that a well regarded university is going to have well regarded researchers as well.