There have been simple and more complex tests to measure whether pollutants have a large effect on asthma and breathing problems in general. In some of the simpler ones, people measured the correlation between days where the pollutants in the atmosphere were at a high level and absenteeism in school and workplaces on those particular days. They used this correlation to point out that the pollutants had a negative effect on the populations surrounding whatever industries.
There are also more specific tests to see how much air someone can breathe in and this can be tested in the conditions which are a concern, namely days when pollutants are highly concentrated, etc. These tests are administered with mechanical devices that measure input and output as well as other things like particulants, etc.