Not by googling "best advertising agency". That search returns lists that were sold, and agencies that are good at being found. Start from the work.
Four steps that do work
1. Collect work you admire and find out who made it. Campaigns from your own sector, but above all from outside it: inside your sector you end up with agencies that have already sold the same solution five times. Award shows, the trade press and agencies' own sites all serve here; the credits are usually listed.
2. Build a longlist of about six. In IKAg-guided processes six is the median. Fewer and you have no choice, more and you will not find the time to look at each of them seriously. Deliberately put one on it that you did not know.
3. Check them on paper before you call. Services, sector, size, group structure and the figures from the annual accounts. That takes ten minutes per agency and usually removes two.
4. Talk to the people, not the management. In a first meeting ask who would work on your account day to day, and have that person explain something. Selling ability and working ability rarely sit in the same chair.
Where to look
IKAg's factsheets are open and searchable per axis: by expertise, by sector, by location and by group. Each agency shows its services, reference clients, awards and key figures from its filed accounts.
Beyond that: ask peers at other companies who they use and what went wrong. That second half of the question is the useful part.
The trap
A longlist that starts from the names you know is not a selection but a confirmation. The agencies you know are the most visible ones, and visibility is a skill unrelated to the work they would do for you.
See also: which criteria to use, how to know whether an agency is good and how many agencies to invite.