well actually all motorcycles are steered via countersteering, and it helps to lean off the bike - the side your turning too, as it weights your turn in - aiding balance, plus it can allow higher speeds during the turn as the tyres remain more upright than they would if not leaning off, allowing more grip.
Couldn't agree with this anymore or said it any better. I could not add anything else except leaning down and kissing the inside mirror should help a bit in some higher speed counter steering.
Riding faster in tight turns is just part of the natural progression of riding a bike. Be careful of those reducing radius turns with limited sight lines.
You learn CS by learning to apply just a little bit of pressure at first and then increasing the pressure and speed. This is one of the first lessons they teach you in the beginners MSCV course.
To practice putting a knee out (not down) you follow the same principle. Start slow and instead of having your inside knee hugging the tank, stick it out just a few inches at a time, going into the turn, with just a little pressure on the bar. It will feel squirrely in the beginning but will get better. Increasing both, a little bit at a time as you get more familiar/experience. Starting in an empty parking lot is a good idea. As you get better, start to slide part of your butt onto the edge of the inside seat and back to center when done.
Be prepared to practice your emergency stops in that turn. This is the next lesson they teach you in the beginner's class. Tip - stand the bike up, and assertively apply back & front brakes w/o locking up. You want the bike to be up and going straight b4 the brakes.
I find the knee helps turn the bike easier due to the clip ons on my L1 750. With clip ons, you do NOT have the leverage you do with handlebars and I find myself using more arm strength than I would on my FJR or SV650. Use to be able to ride from LA to NY non-stop in 36 hours in the dead of winter but now, aFter 2 hours in the twisties, my arms are shot, unless I use my knees more. Just getting old.
Prepping this year to get ready for track days. Pretty sure, my outlook will change once I get on track and "up to speed". Just got my L1 a handful of months ago and the dynamics of this bike is so different than my other ones. Absolutely loving it and can't wait for the track.
Once again, take it slow, within your limits, visibility and level of comfort. Sometimes riding with a more experienced rider will help show you the proper speed, lean angle and body posture.