1st things 1st, Relax.

Understand that "Countersteering is the technique used by single-track vehicle operators, such as cyclists and motorcyclists, to initiate a turn toward a given direction by momentarily steering counter to the desired direction."

Read this:
http://en.wikipedia.org/wiki/Countersteering

Of particular importance to your query: "This process often requires little or no physical effort, because the geometry of the steering system of most bikes is designed in such a way that the front wheel has a strong tendency to steer in the direction of a lean."

Yep, and the bike will follow your eyes. Look where you want to be.

Find a nice big grassy area and gradually increase speed doing L/R turns, shifting weight, applying F&R brakes and generally messing about.
Your position should have bent elbows and a relaxed but firm hand on the controls.

Mild Cyclo-Cross is the best way to improve bike handling skills while the inevitable mis-judgment crash has far less consequence than any pavement sortie.

Look through the turn, relax and let the bike ride itself.

-Bandera