When I took my private checkride 44 years ago next month, my crosswind capability was as close to nil as it's possible to be. The wind seldom blows in Anchorage, so I had the theory down, but not the practice. A 3-4 knot crosswind resulted in crooked landings, and comments from the DE that if I was going to fly in Laramie when I left the USAF, I better learn crosswinds.
I'd been flying at Laramie for several months when my instructor called me to say "today's a great day to learn crosswinds--straight down 21 at 25-30 knots". "How will that teach me crosswinds?" "We'll use 12-30." All the way out to the airport, all I could think was that the maximum demonstrated crosswind capability of a 172 was only 17 knots--how could it be done with a 25-30 knot crosswind?
We took off on 21, but then turned downwind for 30. My first attempt was dismal--couldn't begin to line up on 30, But my CFI then took control, and he showed me that he could do it. If he could, so could I. For the next hour or so, we did a series of landings, first on 30, then on 12, back and forth, until I could handle extreme crosswinds from both sides. All were to a full stop, so that I could experience the need to add more and more control as the airplane slowed, and so that I could learn the proper technique to safely take off again.
I learned several things that day about crosswinds:
+A little extra airspeed (to account for the gusts) is good; too much isn't, because it makes the airplane harder to control as it slows after touchdown.
+No flaps, or at most 10 degrees, is good; more flaps makes the rudder less effective.
+Slipping all the way down final is really uncomfortable and doesn't accomplish much.
+The wind at touchdown is usually less than the wind in the air, even as little as 10-20 feet above the runway. That's why a long slip doesn't accomplish much.
+Crabbing until just before the flare is good, but attempting to "kick the rudder" to line up at the last moment isn't--much better to transition to a slip just before time to flare. +If there's enough rudder to line up with the runway, there's more than enough aileron to stay over the runway.
+Taxiing can be more difficult than landing and deserves every bit as much care.
+Keep flying the airplane all the way to the tie-down, using correct control inputs constantly.
+Taking off requires just as much control input as landing.
That lesson was more than 43 years ago. Since then, it's proven to be one of the most valuable individual flight lessons I've had, allowing me to get into destinations that otherwise wouldn't have been possible.
Cary