Surgery is one of the finer points of medical treatment, and surprisingly not a lot of people know how to do it well. Competent surgeons are few and far between, and you will be showered in praise (and maybe karma) if you're one of the better ones. This guide is intended to teach people the basics of surgery, as well as cover some of the things the wiki may or may not have missed.
This guide doesn't cover IPC surgery because they suck, due to 99% of the tips here being irrelevant on them.
Step one: Operating room setup
The most important part of surgery starts before a patient enters the operating room. Preparation for surgery is very very important, and can mean the difference between life and death, or getting a patient out in one minute or three. A good operating room setup, in my experience, has a nanomed, a beaker and dropper of mitocholide (yell at chemistry), an IV with hydrocodone (yell at chemistry), a duffel bag full of surgery tools including an incision management system (yell at RND), a defibrillator, and the box of blood IVs from the back room.
Taking a nanomed at the start of the round and putting it in an operating room is recommended, as it can save you from having to rush out of the operating room mid surgery for supplies. Taking one of the lesser used ones, such as the one in medbay reception, will make the medical doctors less angry at you.
You can throw the locker of medical equipment and anesthetic tanks in the back room. You'll hopefully never use them.
This step is completely optional, but can save you and your patients a lot of time.
Step two: Pre-Surgery
First off, wash your hands. This prevents your patient from getting an infection, and should be done each before and after a surgery. Clicking on yourself with space cleaner works too, and is a lot faster.
Then you need to decide what type of anesthetic you'll be using. Hydrocodone is ideal, as you can't overdose on it, and it's so very effective. Chemistry has to make it however, so don't count on it early on, or sometimes ever. Morphine is your next best bet, but be careful with dosage, as you can give your patient an addiction or overdose. The tank anesthetic that starts in the operating room is generally considered the worst, as it takes forever to put on and take off, doesn't work on vox and plasmamen, and will start suffocating the patient when it runs out. It can be used for long surgeries that would result in a heavy morphine addiction if you used that, but ether works a lot better in those cases.
If you make a mistake with a surgery step, this means your patient does not have enough anesthetic, and must be given more.
Step three: Actually doing the thing
First off, make sure the patient isn't dead. Unless you're doing surgery on an unclonable race that's passed the defib threshold, revive your patient before operating, not after. For patients in critical condition, it's recommended you stabilize them somewhat, at least enough so they aren't actively dying. You can do this on the operating table, if you have a nanomed.
You'll need to pop the patient in the body scanner in order to see what's wrong with them. If it's only one or two things, you can probably just remember them and won't need to print out a report. If you can't, print one out and keep it on hand.
PRIORITIZE LIFE THREATENING INJURIES!
If someone is actively dying from internal bleeding, fix that first before dealing with broken bones. It'll save a lot of blood and medication that would be otherwise wasted keeping them stable while you fiddle with their femur instead of doing something about their seventeen ruptured veins.
KEEP THE PATIENT STABLE!
This should be obvious, but don't let the guy die. This is mainly a matter of knowing which medications do what, and takes time to learn and master. Alternatively drag a medical doctor in and force them to do it.
LEARN THE SURGERIES!
Everyone starts out new. For beginners, having the surgery wiki page open is useful in a pinch, to know how to fix what (https://www.paradisestation.org/wiki/index.php/Surgery). If you forget a step, you can look at the operating table, which will show you the next step, as well as how much damage of each type the patient has. Eventually you'll memorize the steps for each and every surgery in the game, but the wiki and operating table can fill the gaps in your knowledge until then. If you don't know how to do one specific surgical procedure, like removing terror spider eggs, it's probably just organ manipulation. Most things are organ manipulation.
Step four: The aftermath
Congrats! You now have a healthy, non broken patient. Or do you? It's generally a good idea to quickly scan patients after surgery, to ensure they don't have any further injuries, and that you haven't given them an infection by accident. Messing up a surgery step can cause additional damage, so it's probably a good idea to fix that too before letting them wander off. Time to give them to the medical doctors so they can do the rest.
And if the paramedic brings in another IPC, give them a firm slap and cart the poor sod off to robotics.