All students in a class, pod, or cohort swab their own noses and place their samples in a single tube (that’s the pooling step). The samples in that tube are then run as a single sample, using one test. See it in action here.
If students have trouble performing the swabbing, schools can provide a nurse or other trained staff member to help. However, the test is so easy that kindergarteners typically can do it with no issues.