Countersteer: Think of it as something you do intuitively with body lean. If you lean over to the left of the bike (and hopefully are trying to turn left), your weight shifts onto your left hand and left leg. In essence you are pressing down / forward on the left bar, whether you know it or not, by leaning your body (which is an intuitive action to turn a motorbike).
Now in more extreme circumstances you have to really break down what exactly you are doing. Have you ever tried turning at 90 mph or greater? You'll find that it's quite difficult to rely on bodylean alone to begin the bike to lean because at the greater the speed, the greater the tendency the bike has to stay upright. At these speeds the weight your body naturally transfers into your left arm by leaning left isn't great enough and you have to physically MUSCLE the left handle bar forward to get the bike to begin to lean left. That is the only reason why countersteering feels awkward at high speeds, yet still works, while at lower speeds it is done naturally through body lean. This is something you just have to experience yourself by riding at higher speeds and trying it out.