Before i get into the tips, it's imperative that you ride your bicycle in a safe manner. Do not bomb down descents and always ride within your limits. Let's get to the tips.
Tip #1: Not all Tires are Equal
If you're on a set of worn out gatorskins and thinking about hitting the twisties, I have news for you, you're not going to be living up to your potential. For cornering, you want a high-quality multi-compound and sticky tire. This is absolutely not a place where you should skimp out. Tires are way cheaper than hospital visits.
Tip #2: Get low
Get into the drops and lower your center of gravity to a comfortable place.
Tip #3: Pre-shift your gear for the exit
This may be easier said than done but it's important to have the next gear set up for the exit. The key to fast cornering is getting back on the gas as soon as possible. Take the time before a corner where you'd normally be coasting and set up your gear for the exit.
Tip #4: Avoid braking in the corner
Obviously, if you have to brake to avoid an obstacle, do what you feel is needed. But in a perfect work, braking mid-corner is going to mess up your line and put unwarranted frictional forces on your bike that will lower your maximal speed through. So if you can, brake before the corner when you're going straight and then make your turn.
Tip #5: Don't hang off your bike like a MotoGP rider
Sorry kiddos, dragging a knee like a motorcycle rider doesn't have any place here. Stay planted on your bike for optimal cornering.
Tip #6: Mind the Terrain
Bumps, uneven surfaces, gravel all impact how your corner. All else equal, a corner with a dip in it will be slower than a nice banked corner like you'd see on a track.If you know there's going to be gravel or loose tarmac, it's best to do your turning BEFORE the turn and then when there is a sandy patch go straight, and complete the turn with the remaining amount of road.
I'm going to say this again and again, proper cornering takes practice. Ride within your ability. Go slower than you can and never practice cornering on the open road.