Whenever a school administrator dedicates an aide to a particular student, or classroom, the expectation is that such aide will serve as a facilitator to the student for which they will facilitate. In other words, they are "dedicated" because they are expected to look after any want or need of a specific student or selection of students.
As the mainstream teacher delivers the lesson, the dedicated aid should be providing one on one examples to the student. Let us suppose that the mainstream teacher is introducing a lesson where she is showing the difference between halves and thirds. As the mainstream delivers her lesson, she should also provide the aide with materials to differentiate for the student assigned for the aide. Remember that aides can go as far as having Master Degrees, but if they are employed as dedicated aides, they have to follow the lesson plan of the mainstream teacher.
In the case of a highly-qualified aide, the best course of action is for the aide and the lead teacher to collaborate for strategies and interventions in hopes of creating the best learning experiences for all children. However, if this is not the case, then the best-case scenario is for the lead teacher to create a differentiated instruction center for students who are at the same learning level as the student who has the dedicated aide, and allow the aide to conduct activities geared toward remediation or enrichment as the case may be.