This questions is not very simple to answer, as what role you play and what is expected from you differs on what hospital service you are on, and what is the amount of training you've received prior to going on that rotation.
In general, you'll be rotation through OMS, General Surgery, Anesthesia and Med school (6-year), or Medicine (4-year). Some rotations are longer than others, but there are expectations from every rotation that you should be performing at or above a typical medical resident.
When you are on OMS service, you are expected to be the facial trauma/infections expert, as you will get consulted by a variety of specialities including surgery trauma, ED, medicine, etc. For this service, every program should have some "buddy call" arrangement where you're paired up with a senior level resident that will teach you how to deal with certain situations.
You will also be on general surgery rotations, with most 4-year programs having you complete 4-6 months, while 6-year programs completing 6 months - 2 years. Most of the OMS residents have already completed an intern year prior to doing a general surgery year, so we actually look like rock stars compared to the typical interns coming straight out of medical school.
Anesthesia - 5-8 months rotation. Usually the first 2-4 weeks will be observation, and after that, if the attendings are comfortable with you, will put you in your own room, running the entire case. Anesthesia is extremely repetitive, but once you learn the basics of setting up a room and dealing with random complications that run your way, it's not too bad. OMFS residents generally enjoy this rotation a lot since it gives them a lot more time for other hobbies.
Med school - The 6 year guys go to med school, which can be as short as 12 months (Case Western), to as long as 4 years (UCSF). Since you've completed dental school and already a "doctor", this part of training isn't that bad. It used to be that USMLE Step 1 was the soul crusher, as it was a test that required 3+ months to prepare for, while med students studied 2 years for it.. and OMS residents had issues passing it.. but with the introduction of the CBSE, which is a condensed version of the USMLE Step 1, OMS residents now know what to expect, and those who scored 70+ on the CBSE have no issues passing it now. You are expected to perform above the typical med student.
Medicine - the 4 year guys get thrown into dealing with complicated Medicine patients with medical knowledge that is severely lacking. Dental school and CBSE did not prepare them for this. This is where reading is paramount. Some programs actually have their 4-year guys rotate as a medical student instead of a medical resident because the knowledge curve is too steep. But there will always be upper level residents helping you throughout this process, and as long as you don't ask a lot of questions you can look up yourself, you'll be fine.
Depending on the residency program you are in, you may be rotating through Plastics, ENT, Neurosurgery, Emergency Medicine, and others. As stated above by Setdoc7, you have to be willing to read a lot. Read up on your patients and their conditions. Be ready present for rounds and have tentative plans. Your plans will not always be correct, but your upper levels and attendings can always steer your reasoning in the correct way. If you come unprepared, not only will you look bad, but it will make the entire OMS service look bad.