Basic common sense is not enough when it comes to staying safe around a tractor-trailer. Really, semi-truck safety is about as different from normal traffic safety as bicycle safety is from motorcycle safety. You need to protect yourself and you need to make sure that you know your way around a tractor-trailer if you hope to be safe out on the road with them.
Keep Their Mirrors in Your Sight
As a general rule of thumb, if you can't see a trucker's mirror, then they can't see you. There are ways to adjust your rearview mirrors in a car in order to eliminate your blind spot, but truck drivers do not have this option. If you're coming up behind a truck, make sure that they can see you in their mirror if you're going to be anywhere where they can potentially run into you.
If you assume that a compact car is going to stop at that intersection like they're supposed to, and they don't, you'll probably walk away from the accident and they'll be found at fault in the accident. If you assume that a truck driver is going to stop at that intersection, and they don't, you're going to be lucky to wind up in the hospital. Trucks are big, massive behemoths. They're a necessary component of American industry, but they don't stop on a dime, and if you trust every truck driver you see, then you may wind up in a serious accident with one of them. Practice defensive driving with every other car on the road, but especially truck drivers.
Six Seconds of Space
If it's raining out or if conditions are otherwise wet or adverse, then you're going to want to give truck drivers six seconds of space between you so that they have more time to react. You should also give them this much space when driving at highway speeds. You don't need to be quite so cautious in city limits, generally speaking, but the more caution you exercise, the safer you'll be. Stopping a truck suddenly can be tremendously dangerous, and accelerating quickly can be impossible, so semi trucks just don't have the split-second reaction time that you get on a smaller vehicle. Give them time and space to drive safely.
Maybe you don't like to poke your nose into other people's business when you see someone drinking alcohol by the pool or smoking in a no-smoking area. Maybe you have a sort of Libertarian stance on things like drugs and other minor offenses. Don't be so liberal when it comes to truck drivers who are driving unsafely. As the saying goes: the life you save might be your own. Don't hesitate to report an unsafe truck driver if you see them swerving or otherwise driving recklessly. You may wind up getting a truck driver slapped with a penalty or even having their license suspended, but you may wind up saving their life, and whether or not they appreciate that, it's the right thing and the safe thing to do, so don't worry about being "a snitch." This is your life and your safety we're talking about, not the drug game as explained by a rap album.