It's time I ask some questions.. mostly bike questions.....

I am not the resident bike expert around here but I'll take a shot at questions;

1. You kind of want to power over the top of a hill to start your downhill. But I don't change into the big ring to do that as the stress of pushing on that chain at the top of the hill can cause the chain to fall off. I change gears carefully as I'm coasting down the hill to the gear that I thnik I'll need when I hit top speed. As I hit that speed (or come down to the speed that my top gear goes) I begin my pedaling again at around 90 cadence and go from there.

2. It does sound like you need to work on your base and ride a lot more. Generally, beginners who work a properly structured training program improve quickly. I wouldn't be disappointed it you can't get to 18 mph average. Take pride in the fact that you are out there doing it and you are improving.

3. I have never taken a bike handling course and I don't know much about them. Though, I think you can learn a lot by just reading Tri books like Going Long and asking questions on this board.

 Good luck with the training.

Yes, I do think that you will learn a lot by riding in a group. You should gain quite a bit of speed  just from riding more, but this will be even quicker if you have people who can help point you in the right direction.  In addition to improvements in fitness, you'll gain a good deal of speed from technical improvements in shifting, cadence, pedal stroke, and things like judging how to best take hills of different size.

Also, remember that your overall speed in a race may be considerably faster than your speed in training.  I never have an overall average speed (be it bike, swim, or run) after a workout that is as fast as my total performance in a race. 

For hills, ideally you don't let up as you go over the peak.  Keep pushing the gears up as you start to descend so that you can get to max speed down the hill ASAP.  If you get up to speed and find that you are spinning in your highest gear, put your feet in the 3 and 9 position and make yourself small to minimize wind resistance.  Start pedaling again on the flat or next uphill section as soon as you can get some pressure on the pedals at a reasonable cadence.

If this is your first season of doing tris, I'd advise against setting any speed/time goals.  If you do, and you don't meet them, instead of being happy that you're now a triathlete and basking in the glow of your first finish, you'll instead be disappointed. 

You can change gears while going downhill, but you have to turn the pedals around. 

I'm no expert on the bike (and everyone knows that!), but like the other posters said, you should use the downhills to help you up the uphills.  Here's what I do:

On the downhill, I gear up into my big chain ring, and then gear up until I'm in the gear I think I'll need on the flat (for me, that's around the 5th gear).  I 'soft pedal' until it starts to flatten out, and then I add more energy to the pedals to hold the momentum as long as possible, dropping down to my small chain ring first, and then gear down as needed, while keeping my effort level even and cadence high. 

I agree that you have to "attack" the top of the hill, and I don't allow myself to even think about coasting until I'm well over the top and geared back up into my big ring and 5th gear, and ready for the next hill.

Fortunately, I get to practice this where I live on pretty much every ride, since I'm surrounded by lovely rolling hills. 

Time in the saddle, cowgirl.  Learn to trust your bike, and you on it.  You'll get more comfortable with the balance and leans for turning, as well as standing on the pedals for immediate power/uphill climbs.  Become one with your ride.

As for shifting, try to anticipate the climb.  Downshift a bit ahead of time (but not too early), so you're not caught at the base of a hill trying to get into a gear you can handle.  This kills your mojo and can cause the dreaded and embarrassing "clip fall".   Once you handle the climb, if you're not inclined (pardon the pun) to rest a little, and depending on the length of the descent, you can rapidly shift to large chainring and max gears.  So long as you "catch" the gears, keep pedaling.  If you're flailing around wildly (remember when you were a kid and only had one speed), coast.  You've maxed out and the flailing can cause you to lose control.  With experience, you'll know when to begin picking up the pedaling again and as the route flattens, to downshift to a comfortable rythym.

Don't forget to smile (relaxing technique) as you climb, and to yell like a kid when you go down hill really fast, i.e. have fun.

just a little addition to that comment...   you do have to pedal a little when you change gears while coasting so the chain can be moved to the gear you desire.  If you dont, when you go to pedal up the next hill and you put tension on the chain, you could break the chain because of the awkward angle of the chain.  I hope this makes sense,  i reread it and it makes sense to me, but as a beginner cyclist, i am not sure that you would understand.  If you have questions, just ask.

 Josh

Yeah...that's what I meant to say.

It'll get better.  Get out and ride (or stay inside and ride). 

You'll see some pretty dramatic improvements in the first couple of months.  My first rides last year were 14 mph (give or take) and I raced an OLY (40K) in June at 20+ mph and a HIM at 20 mph.  Getting from 17-18 up to 20 will be much slower than 14 to 17. 

It's OK to spend time in the small chainring.  (Really, although I would have never tried that 25 years ago).  You'll probably want your pedal cadence in the 85-100 rpm (shoot for over 90).  Pick a gear that keeps you pedaling that fast.  As you come up a hill, you'll need lower gears.  On the downhill, higher ones. 

Go on some beginner group rides (usually advertised as "no-drop".  You'll enjoy the company and learn a lot from the other riders. 

As for lessons and steering.  You could hire a private coach for some basic technique and drills.  As for your question about leaning versus steering, yea, it's a lot like motorcycles where you'll want to lean. 

1. Ride up a hill in whatever low gear you can handle.  Gear up about 100 meters before you crest the hill.  Change into as high a gear as you are comfortable with going downhill.  You have to pedal to change gears or the chain will not be moving to be thrown up of down, so no coasting.  Anyways, coasting is counter productive as the muscles cool down.  Keep spinning. 

2. If you you learn to use your full range of gear properly and do not coast at any time, you should increase your cycling effectiveness by a wide margin.  

3. A bike handling course is always worth the time and money for any rider!  Contact your local cycling club and find out what kind of courses they offer.  

4. Practice your spinning on a trainer.