Simple until a car turns left infront of you leaving you 0.3 seconds to do anything.
#1 rule of riding: look where you want to go not where you don't want to go.
To initiate Push forward on the handle bar on the side you want to lean.
Lowering the inside elbow/shoulder slightly helps the bike carve the corner.
Slight forward pressure through the corner on the inside handlebar.
Look through the corner.
Turn in slightly with opposite force to stand it up.
The bikes geometry will tend to self center and steer the bike straight.
Braking hard also wants to stand the bike up making it difficult to bake and turn at the same time.
When countersteering You are forcing the handle bars opposite the direction of the turn making the bike fall into the corner.
The faster you go the the more inertia you build up and the harder it is to turn in and change your current vector.
If you don't turn or stop you will continue on your current vector Like Joey Dunlop vs the tree.
Basically you don't have time to think about whats happening as it happens and it all comes down to muscle memory developed through years of riding as many varied disciplines asmuch as you can.