Surgery
All surgery requires the set of medical tools in the Operating Theatre, along with a table (a surgical table gives no negative results). For the most part, only medical doctors and the Chief Medical Officer can perform advanced surgery.
Surgical Tools
Surgical tools can be found in surgery and robotics. Additionally, cargo can make them with their autolathe. It is best to keep surgical tools in their proper places so your fellow crewmembers can use them when they need them. The following are the standard surgical tools most doctors will need:
MMI (For Robotics)
Surgical drill
Scalpel
Circular saw
Hemostat
Cautery
Retractor
Drapes
How to set internals
To set internals and make your patient sleep you need to first remove any item from their back. Once done you need to put a breath mask on them and then put the anesthetic tank onto their back. Once it is on their back you can put them on internals by clicking "set internals" on the same menu you used to put the tank on their back. Once done your patient should fall asleep. Remember to use a proper anesthetic mixture, as pure N2O will suffocate the patient.
Eye Surgery
Fixing Blindness
Step 1: Place the patient onto the operating table.
Step 1.5: Use a tank of anesthetic and a breath mask to make your patient sleep. (Optional)
Step 2: 
Place drapes over the patient's eyes.
Step 3: 
Aim for the patient's eyes, and cut the skin around them with your scalpel.
Step 4: 
Use your retractor to lift up the eyes.
Step 5: 
Use your hemostat to stop any potential bleeding.
Step 6: Use hemostat again to fix the patient's eyes.
Step 7: 
Use your cautery to seal the wound.
Step 8: Wake up your patient, congratulate them on their new vision.
Brain Surgery
The nerds next door may be doing rocket science, but hey, it's not exactly brain surgery.
Step 1: Place the patient onto the operating table.
Step 1.5: Use a tank of anesthetic and a medical mask to make your patient sleep. (Optional)
Step 2: Place drapes over the patient's head.
Step 3: Aim for the patient's head with your scalpel to cut back the flesh.
Step 4: Clamp bleeders with the hemostat (or use wirecutters).
Step 5: Retract tissue with retractor.
Step 6: 
Cut the spine with your saw.
Step 7: Extract the brain with the hemostat (or use a crowbar).
Step 8: 
Deal with the brain, typically by putting it in an MMI and then giving it to a roboticist.
Step 9: 
Morgue the body.
Putting a brain back in
Step 1: Place the patient onto the operating table.
Step 2: Cram their brain back into their skull
Step 3: Usually, you take the body to be cloned.
Implant Removal
Step 1: Place the patient onto the operating table.
Step 1.5: Use a tank of anesthetic and a medical mask to make your patient sleep. (Optional)
Step 2: Place drapes over patient's chest.
Step 3: Aim for the patient's chest with your scalpel to cut back the flesh.
Step 4: Clamp bleeders with your hemostat.
Step 5: Retract skin with your retractor.
Step 6: Extract the implant with your hemostat.
Step 7: Close the wound with cautery.
Appendectomy
If it's useless, tear it out
Step 1: Place the patient onto the operating table.
Step 1.5: Use a tank of anesthetic and a breath mask to make your patient sleep. (Optional)
Step 2: Place drapes over the patient's groin.
Step 3: Aim for the patient's groin, and cut the skin with your scalpel.
Step 4: Use your hemostat to clamp any bleeders.
Step 5: Use your retractor to open the incision.
Step 6: Use your scalpel to sever the appendix.
Step 7: 
Use your BARE HANDS to pull out the appendix.
Step 7.5: Dispose of the newly extracted appendix / eat the appendix / force feed it to the patient. (Optional)
Step 8: Cauterize the wound with the cautery.
Step 9: Wake up your patient and congratulate them on overcoming appendicitis!
Xenomorph Removal
GET IT OUT OF ME!
Step 1: Place the patient onto the operating table.
Step 1.5: Use a tank of anesthetic and a breath mask to make your patient sleep. (Optional)
Step 2: Place drapes over the patient's chest.
Step 3: Use your scalpel to cut through the chest.
Step 4: Use your retractor to retract the skin.
Step 5: Use your saw to cut through the chest.
Step 6: Use your hemostat to pull out the larva.
Step 7: Close the wound with cautery.
Step 8: Congratulations! Your patient lives!
Lipoplasty
Why did I eat three whole pizzas?
Step 1: Place the patient onto the operating table.
Step 1.5: Use a tank of anesthetic and a breath mask to make your patient sleep. (Optional)
Step 2: Place drapes over the patient's chest.
Step 3: Use your scalpel to cut through the chest.
Step 4: Clamp bleeders with the hemostat.
Step 5: Slice up the fat with the saw.
Step 6: Remove the fat with the retractor
Step 7: Close the wound with cautery.
Step 8: Feed the patient his own fat as a lesson in vicious circles (Optional)
Plastic Surgery
I need to disappear forever!
Step 1 - Place the patient onto the operating table.
Step 1.5 - Use a tank of anesthetic and a breath mask to make your patient sleep. (Optional)
Step 2 - Place drapes over the patient's head to prepare for plastic surgery.
Step 3 - Use your scalpel to make an incision in the head.
Step 4 - Use your retractor to retract the skin around the incision.
Step 5 - Use your scalpel to alter the patient's appearance.
Step 6 - Use your cautery to mend the incision you made.
Step 7 - Send that stranger to the HoP to finish his induction to the witness relocation program.
Gender Reassignment
For when something other than xeno scum is trapped in your body
Step 1 - Place the victim patient onto the operating table.
Step 1.5 - Use a tank of anesthetic and a breath mask to make your patient sleep. (Optional)
Step 2 - Place drapes over the patient's groin.
Step 3 - Use your scalpel to cut through the groin.
Step 4 - Clamp bleeders with the hemostat.
Step 5 - Use the scalpel to carefully reshape the patient's... body. ***This actually applies their body-weight in estrogen or testosterone instantly, the scalpel acts as a giant syringe in this case.
Step 6 - Close the wound with cautery.
Step 7 - Perform plastic surgery to acquire a new gender appropriate name (Optional)
Cavity Implant
My god, he's a ticking timebomb!
Step 1 - Place the patient onto the operating table.
Step 1.5 - Use a tank of anesthetic and a breath mask to make your patient sleep. (Optional)
Step 2 - Place drapes over the patient's chest.
Step 3 - Use your scalpel to cut through the chest.
Step 4 - Clamp bleeders with the hemostat.
Step 5 - Use your retractor to pull back the skin.
Step 6 - Use your scalpel to cut through to a cavity.
Step 7 - Carefully place an item in the cavity / Use your hands to check for items in the cavity.
Step 8 - Close the wound with cautery.
Ghetto Surgery
It is possible to perform surgery with improvised items, but the chance to complete each step will greatly decrease.
Generic steps:
Place drapes: drapes, bedsheet
Make incision: scalpel, kitchen knife (65%), shard (45%)
Clamp bleeders: hemostat, wirecutters (60%), cable coil (15%)
Retract skin: retractor, screwdriver (45%), wirecutters (35%)
Close incision: cautery, welding tool (70%), lighter (45%), match (20%)
Saw bone: circular saw, hatchet (35%), butcher's cleaver (25%)
Plastic surgery:
Reshape face: scalpel, kitchen knife (50%), wirecutters (35%)
Xenomorph removal:
Xenomorph removal: hemostat, spade (65%), minihoe (50%), crowbar (35%)
Brain removal:
Extract brain: hemostat, crowbar (55%)
Slime core removal:
Extract core: hemostat, crowbar (100%)
Eye surgery:
Fix eyes: hemostat, screwdriver (45%), pen (25%)
Gender reassignment:
Reshape genitals: scalpel, hatchet (oh my God) (50%), wirecutters (35%)
Implant removal:
Extract implant: hemostat, crowbar (65%)
Lipoplasty:
Cut fat: circular saw, hatchet (35%), butcher's cleaver (25%)
Remove fat: retractor, screwdriver (45%), wirecutters (35%)
If you can't find an operating table, have no fear, you can fix someone up anywhere! Any table or bed will do, and even the floor if you have no other choice. It will reduce the chance of successfully completing a step, however.