The Fairway Pirouette
My outboard is on the right side of the boat
Mount the rudder/tiller in the slip.
If you back to the left, leave the OB alone, and use just the tiller.
If you back to the right, you may find that cocking the OB to the right, maybe 45°, when you're almost half-way out of the slip will defeat the OB's desire to pull you straight back into your dock neighbor's stern, and gets you lined up in the fairway . When shifting into Forward, straighten the motor head, and Bob's your uncle.
If the wind is coming from the direction you want to ultimately point to move out the fairway, you may discover that the bow wants to blow downwind, and prevent the boat from pivoting: throwing the OB over to the stop and adding a little more throttle will pull the stern downwind (deeper into your fairway) and allow you to point into the eye of the wind, so that you can shift to Forward and get some weigh on before the bow blows off and drives you into the finger once you shift to Forward and open up the throttle.
In general, when leaving, use only enough power to overcome wind & current: more than you need is just extra energy that you must control while executing your maneuver, and can get you into trouble, and having to do only one thing at a time is nice.
Coming into your slip, keep your speed well down, and if you are coming down the fairway with a significant downwind, you may find that swiveling the OB really throws the stern around to get you lined up with your slip, esp. if your slip is to the right. But you have to be ready to quickly straighten it just as you get lined up, or shift into neutral, the moment the stern is lined up, or you'll get too much of a good thing.
Things are happening quickly at that moment, so I'd experiment with smaller movements of the OB at first, until you can do it in your sleep, before throwing it around like you've been doing it all your life.
Fair Winds,
Jeff