Welcome to the community! The Handbook will be a great resource. In the meantime, I'll do my best to explain here to get you started. To preface, this is if you are operating with the sled on your left side - do you operate on your left (regular) or right (goofy-foot)?:
The two thumb (wingnut) screws are your "in and out" adjustments, which balance the sled away from or towards your body.
The two knurled screws are your "side to side" adjustments, which balance the sled left or right of your body.
Start by making sure your side-to-side screws are "zeroed out" by turning the bottom screw all the way in (you can tell if it's in or out by checking if you are making threads appear or disappear on the socket - you want them to disappear), then out a quarter turn so the screw doesn't bind. You want the bottom screw all the way in so the arm stays connected to the socket - if it's all the way out and doesn't have any threads to grab, it could fall off. Next, turn the top screw all the way in, then out 2 and half turns to start. A "turn" on the knurled screws is as much as you can do with your thumb; not a full rotation.
You mentioned your sled is going away from you and to the right; at this point it may be doing something different side-to-side after resetting the knurled screws, and it may feel different than last time in-and-out based on how you turned the thumb screws.
Make sure you are standing straight with good posture, and not leaning to compensate for the rig. In essence, you want the rig to "lean" to you via the screw settings, not you leaning to the rig. Put the rig on your centerline, and turn your pelvis at a 45 degree angle towards the sled (think camera pointing forward is one straight line, your pelvis is another straight line, turn that 45 degrees to the line of the camera). You want to keep the sled as close to your body is as comfortable without hitting the sled on your knee (or your face - ouch!) This is the position you will aim to keep while operating as much as possible. Also make sure you have a good fit with your vest - you want it sitting snug on your shoulders, sitting on you straight (make sure you have your velcro even on both sides - having one side tighter than another will make the vest tilt under load), and the waist portion should be centered vertically on your pelvic bones.
While in that position, let go of the sled slightly by opening your hands - don't move your arms away so you can catch the sled if it violently moves away from you. Take note of what the sled is doing when you let go: falling into you, falling away from you, moving left, or moving right.
If it's falling into you or away from you, you'll need to adjust your in-and-out settings, which are the thumb screws. Take a look at the arm in the vest without wearing it and turn the screws to better understand how turning the screws affects the balance. If you turn the top screw in and the bottom screw out, it will make the rig lean into you - what you want to do if the rig is falling away. If you turn the top screw out and the bottom screw in, it will make the rig fall away from you - what you want to do if the rig is falling into you. These screws don't need to be wrenched down tightly; finger-tight works.
Similarly, it will help to look at the side-to-side screws without wearing the vest to understand how they operate too. My vest doesn't have the knurled screws, but is altered via a T handle wrench, so I'm not positive which way (up or down) you'll want to turn the screws for the desired effect, though you'll be able to tell quickly by looking at it. You'll only deal with the top screw here as you want to leave the bottom one in as much as possible for more connection strength. If the sled is falling to your left, you'll want to turn the screw so more threads appear, which will pull the sled to the right. If it's falling to the right, you'll want threads to disappear, which will pull the sled to the left.
Do both the in-and-out and side-to-side adjustments until the sled sits in the aforementioned sweet spot without touching it, while maintaining good posture.
Hopefully that all made sense; there are pictures in the book that will explain better!