Hi there! Compounding can occur in various settings including community, hospital, physician offices/clinics, and outsourcing facilities. You may be able to find internship opportunities in those settings by contacting your pharmacy school and seeing if they have rotation in one of those facilities. Usually, pharmacy school offers compounding as a general curriculum requirement as well as an elective in your 4th year rotations which may give you further experience.
Post-grad residency for compounding is typically not required. Compounding pharmacists can be hired by drug companies as well as compounding facilities listed above. In addition, you may be able to find these outsourcing facilities through FDA's website to tailor the search to those facilities in your area.
Say what? Actually most places have a waiting list for internships. OP should expect to have to apply and interview at several different places, and expecting it to take quite some time, before s/he gets an internship. The OP will probably have better luck just applying for a straight part-time technician job.