I definitely understand your fear about anesthesia, and believe it or not, you are just like almost every patient I talk to about surgery - you are more afraid of the risks of the anesthesia than you are of the actual surgery! When you stop and think about it, this is only natural, because "going to sleep" with a general anesthetic represents one of the scariest things most of us can think of. It represents a total loss of control over one's fate, and putting that control in the hands of people you HAVE to trust if you are going to have surgery: the anesthesiologists and the surgical team. I would be at least a little afraid of that myself, especially if I didn't know much or anything about medicine, surgery, or anesthesia. I think everything you are hearing about this from medical professionals is accurate and well-meaning, but I can also see how that still might not be very reassuring. Everyone says "oh, don't worry about that, you won't die," or "you have a greater risk of getting struck by lightening than dying from a breast augmentation," or "as long as you are healthy the anesthesia is very safe." All of those things are pretty much true, but I can see how they can either minimize your concerns or at the very least not provide a sufficient answer for you and be unsatisfying. So, at the risk of saying too much here in a long-winded response, I'm going to give you a very thorough response to your question, and I hope that it helps allay your fears.
You have really asked 2 things here in your post: 1) you've essentially asked about some idea of the level of risk of general anesthesia for breast augmentation, and then 2) you've asked what you and your doctor can do to lower those risks in your case. So let's look at the first part first.
From the standpoint of risk with general anesthesia, something many people may not realize is that there is actually a very well defined, well-tested, tried and true process on the part of both anesthesiologists and surgeons to assess and manage this risk. While we may not go through and discuss each assessment and analysis we make at the time with the patient, much like driving a car - we don't say "OK, I'm turning the key here, now I'm putting it in gear, now I'm stepping on the gas, etc., etc," we just do it, we just drive the car - so it is with our assessment of risk, especially in people who don't have a lot of factors to consider, like younger, generally healthy people, we do it as we're interviewing and examining you and reviewing your health history. Specifically, the anesthesiologists have a reproducible, quantifiable method for assessing risk for general anesthesia that has been used for over 50 years, and each and every patient that undergoes a general anesthetic is classified according to this schema. It is called the "ASA (American Society of Anesthesiologists) Classification, and it uses very specific criteria to classify each individual patient undergoing an anesthetic from Class 1 to Class 6. In a nutshell this classification uses things like general health status (smoking, alcohol use, any diseases or medications, weight/obesity, illnesses, like diabetes, high blood pressure and severity of those, and other factors like that) together with nature of the surgery (elective, emergency, organ procurement for donation, etc) to make a determination of ASA class for the purposes of evaluating (and managing) risk. Doctors also take into account a person's age, the specific nature of the surgery, duration of surgery, and factors like that to round out the mathematical and subjective assessment of risk. In general most studies that have looked at this in terms of mortality (death rate or risk), the numbers have been very roughly around 0.03% (3 out of 10,000) chance of death for someone in ASA Class 1. This is a somewhat rough number, as there is a lot of variability, and like I said, things like age and type and duration of surgery factor in as well, but at least this gives you some idea other than just "don't worry, the chance is low, you won't die." I would venture to say that for most young healthy nonsmoking patients without any medical conditions like asthma, diabetes, etc. undergoing only elective breast augmentation, which is typically a brief 1 - 1/2 hour procedure that loses very little blood and requires generally light anesthesia, they would wind up easily in ASA Class 1 and have extremely low risk for death with anesthesia. It would be even lower from a purely surgical standpoint. Beyond this, you will have to review your own individual medical history and risk profile with your anesthesiologist and surgeon in order to get a more specific idea of your personal risk.
With regard to things that you and/or your surgeon can do to lower your risk, I think the above discussion gives a clue to at least some of those. Clearly, healthy people who are not obese, who don't smoke or drink excessively or use drugs, who have good control over any diseases or medical conditions they might have, and who have straightforward surgical plans for breast augmentation will have the lowest risk. Thus, things like stopping smoking if you smoke, avoiding excessive alcohol or drug use, maintaing a healthy weight and body fat percentage/BMI, following any doctors' orders to control medical conditions, and exercising to keep fit are all things you can do to lower your anesthetic risk, and in particular your (likely extremely low) risk of an anesthetic death. Your surgeon may also include some other things in the mix to lower risks as well, like preoperative hydration with a specially formuated pre-op beverage (like ClearFast®, which I use for my patients) which lowers things like preop anxiety (thus the possible need for deeper anesthesia or greater doses of anesthesia), risk of intra- or postoperative nausea and vomiting, and hypo- or hyperglycemia, use of preoperative premedication with acetominophen (e.g., Tylenol) which can also decrease overall anesthetic requirement, and thus risk, or certain blood pressure medications or other drugs administered by the anesthesiolists at the start of the procedure which can also lessen risks. Additionally, there are also some things the surgeon can do to lower other risks too, like risk of infection, but those aren't really involved with risk of anesthetic death per se, so we won't go into those here other than to just make you aware that risk avoidance is a very real thing that we surgeons think about (or shoud), and there are LOTS of things that we can do to lower overall risks for our patients and get reliably good results safely.
I know this is a long-winded response, but I hope it was interesting to you and helped make you feel better than just saying "oh, don't worry about it, the risk is very small." Lastly, make sure you also go to a board certified plastic surgeon for your surgery (and board certified ANESTHESIOLOGIST as well), as this has actually been shown to give you a better statistical chance of a safer operation with a better outcome, not because we are all geniuses or the only ones who can do this surgery, but because we are a select group of surgeons who have demonstrated a commitment to things like safety and best practices, and with anyone else you don't get that reassurance, so you just don't know. Best of luck to you!