I've seen 5mph corners. I've shot through them at close to 20. 

As a rule 2.5 times posted is damn near or at (and in some cases just beyond) the limit. I have tripled a few 20's and ADDED 10 (not advised, all kinds of shaZam! scrapes, and pegs fold up, even hanging off like a monkey) 

I about pooped myself there, but it was a blast.

Try taking it at the normal speed (or so) and hitting every apex first boy racer. Yeah it's harder than it looks.

Brake to the speed you want for the turn, or maybe a hair faster.  After braking but before turn in, there is a settling period.  During the settling period, I move the center line of my body (both hips and shoulders) to the inside of the bike, even if it is just an inch, weight the outside footpeg (Note: I keep my hips and shoulders to the inside of the bike until I am through the turn all the way and the bike is standing up straight, no matter what).  You may have to counter balance the bike a bit before turn in by leaning the bike towards the outside of the turn, but only before you lean it in to the curve.
Countersteer by pushing with your inside hand.  Keep the out side arm as relaxed as possible.  And eyes.  Always looking through the turn to the exit and then past it.  Make the turn in as late as you can to see farther into the turn towards exit.  The most important thing at this point is to roll the throttle on or keep some degree of throttle on.   Never just roll though a turn leaned over.  Throttle will settle the bike and the susupension.   Keep rolling it steady. . . then countersteer with the outside hand, stand the bike up, move back to center and give it WFO throttle until you have to brake again.

Thanks everyone for all of the replies and the advice.  I think I'll practice the apex thing, sounds like good turning practice without having to go crazy speeds.  Jake D thanks for the play by play.  I am doing most of that, but I'm not shifting my weight at all (at least not consciously).  I guess  "Make the turn in as late as you can to see farther into the turn" is where the idea of "flicking the bike into the turn" comes from?  Makes sense.

I have a wife and 4 kids so I'm not interested in going MotoGP around here or anything.  Just wondered about how to take the corners with a little more spirit when the mood strikes me. 

Jake D  Awesome, man!

I forgot the simplest of things - choosing your line:

Start from the outside of the turn, pick your apex, and drift out to the outside of the turn after the apex, rolling on the throttle.  If this has already been covered...my appologies. (I'm lit)

Thanks scratch...I'm about to start getting lit.  Late start for a Friday, but it's been a rough week.

Short week!  Five days of work crammed into four!  Whew!

Work for Lowes. Every day is like a week of it's own.

(A week spent in a prison cell with five huge men, all named Bubba.)

Doubling the posted speed limit in corners is really not the best advice to be giving to a noob sportrider with a wife and 4 kids--or for anybody for that matter. 

Like somebody said, good judgement trumps good skills:    http://home.comcast.net/~alan.s.moore/vp/vanish.htm

Excellent link!  I recognize those roads as Hwy 9 and Mt. Hamilton Rd!  The author owns an '89 RZ350...Yamaha stopped making those in '85.

Thanks Gisser, that page on the vanishing point and the page it links to with pictures was very helpful.  I will definitely be thinking about the VP on my next ride.  Don't worry, my family is always in the back of my mind when I'm riding.  I won't be doing anything stupid.  This is a risky enough pasttime with all the idiots out there (it is way too easy to get a license in this country). I'm not about make it riskier on purpose.

You sound like a wise rider.  Kudos to you!    You will have a long riding career!