We can't cover everything about boat docking in one sitting, but I think you'll be surprised at how many of the basic principles of close quarters maneuvering are embodied in the example docking which I will be discussing shortly. First let me answer these two questions: Is this boat handling exposition for novice boaters? Yes, absolutely. Is it for expert boaters? Yes. Experts often pilot their boats by an instinctive feel, and are delighted finally to see and to understand why it is that what they do works so well.
That brings up another important point. Learning to dock is done on the water, in our boats, not by reading about it here. Book learning and good teaching are important, (I would say crucial), and allow us to focus our minds more quickly and clearly than just by using the trial and error method. However, ultimately, we must accept the responsibility ourselves for learning the mechanics and feel of boat handling, for what works and what does not, for us and for our particular boats, by actually doing it.
Port-side-to -- a docking dissected
For the present purposes, I'm going to assume calm conditions, and not factor in the effects of wind. Wind is probably the hardest thing to contend with, when docking a boat, but there's a lot of water to pass under the bridge before that discussion, so I'll leave it out for now. Many of the techniques we're about to cover, however, will also prove useful in coping with wind.
What's your angle?
The first thing to notice is that this boater is coming in at an angle. This makes it much easier to aim for a particular spot, and to bring the boat in close to the dock without scraping. There isn't always enough "sea room" to do this, but when possible, using an angled approach makes life simpler.
Coasting and the power turn
Secondly, think about what throttle setting you would use at the beginning of the approach. A calm, orderly, accurate docking will usually require the slowest speed available, but on many boats, even idle speed is so fast that they have to coast. However, coasting is when "steerage", the ability to steer, is at its minimum, because either i) there is no discharge current from the propeller to amplify the effect of the rudder, or ii) with inboard/outboards, most of the steering "authority" simply vanishes when the transmission is in neutral. So, even when going very slowly, we still steer with power, when necessary. You could wish that the boat would just drift all the way in without wandering off course, but with many (not all) boats, that's all it would be: a wish! If in neutral gear, give a short shot of forward gear (generally only at only idle speed, but use more if required), to steer the boat back onto course, and then coast for another distance. If already in gear, and the boat is still getting away from you, open the throttle briefly for a few moments until you regain control. The general principle is that the sharpest turns can be made when the boat is going extremely slowly, because it will skid less widely through the turn. Yet, the turn is often best done with power, so reconciling these two conflicting demands (minimal power to go slowly, more power to steer), means using power intermittently, and then using it vigorously enough to perform the maneuver.
Keep up the momentum
The next thing the boater will do, as the dock draws nearer, is to start to turn the boat. However, this is also about the time that he or she wants to decelerate to a stop, in reverse gear. While slowing down, the vessel may be hard to steer. This is largely because very little water will be flowing over the rudder (or worse, over the outdrive leg of an I/O).
Fortunately, boats in motion have momentum: once in motion, they tend to continue in motion, and once turning, they tend to continue to turn. This sometimes confounds the less skilled skipper, and yet momentum is exactly what to use when all other steering options fail. At just what point to turn, and how hard and for how long, I cannot say. It will vary by boat, by the prevailing conditions, and even by the skipper's individual style. But the boat must turn, and often this will be done by a brief, firm pulse of power, with the wheel hard over. Part way through the maneuver, by which time the boat is in reverse gear, the only thing that keeps it turning, and that keeps it sliding sideways towards the dock, is momentum. The skipper did this on purpose, took a run at it, so to speak, albeit very gently and cautiously, and then skidded the boat into its slip.
A walk in the dock
One final thing: it is very common for propellers to thrust asymmetrically, more on one side than the other, and in some boats the effect is often especially strong in reverse gear. It's called "walking", because it almost seems as if the stern of the boat wants to walk sideways, when you first engage reverse propulsion, rather than go backwards.
It's because of this effect that we are discussing specifically port-side-to docking. Right hand propellers walk the stern to port, in reverse (a minority of propellers are "left hand" - for them, this whole discussion is a mirror image). So, not quite as much turning momentum is required as would otherwise be. Asymmetrical thrust can be a nuisance, so at least in circumstances like this when it can be helpful, we might as well avail ourselves of it.
There is no conclusion to boat docking. I have yet to hear the final word, and I've probably discussed and studied it more than most. Even if this port-side-to docking were all there was to know (and it's not, it's just the barest beginning), one could still spend a lifetime honing and refining the skills and techniques it requires, and the better feel for boat handling thus engendered would spill over into all of our other close quarters maneuvering. And my wish for us all is that we continue to hone and refine for a long, long time, and that we love every minute we spend doing it!