Not everyone needs or wants to do an internship or a residency. If you think you might, talk to those that have gone before (your clinicians) and those doing it now (interns and residents).
Vet school unleashed – internships and residencies
Veterinary Internship/Residency match program : https://www.virmp.org/
AAEP Avenues for equine private practice internships (you will need to register)