Tips on shifting between chainwheels?

Same for me.  You'll have to learn to anticipate your shifts to make sure you are in the right chainring.  Use the cogs on the back to finetune the effort.  I almost always shift one to two cogs on the back when I shift chainrings.  I will sometimes do this simultaneously when just cruising on the flats or coming to a light.

If you have a double, you will find shifting is always a bit of a "jump".  I suppose that's a benefit - or so I hear.  The biggest thing that helped me was realizing which gears I really need. There is a lot of overlap and some essentially unnecessary gears.  I learned with my set-up that the only gears I really need in my "easy chainring" are the easiest 4.  The rest are virtually duplicated in the big ring.

Sheldon Brown can help show you the gear ratios here: http://sheldonbrown.com/gears/

So, long answer to question, I always put myself about in the middle gear before I switch and then shift a few gears in the back to recover.  I think that's instinct.  While it feels drastic, it's where I want to be and also I am less likely to drop a chain.   So, I spin like a crazy person for a second but then shift up a couple of gears and I'm fine.

But yes, you must anticipate this coming to a hill and suffer the spinning for a little bit until you know the course better or can push a bigger gear!

I wouldn't shift front and back simultaneously.  Sounds like a sure recipe for dropping a chain.

Edit:  I add that first bit as an answer to a question which you didn't really ask.  But what I am saying is that you probably don't have to switch chain rings as much as you'd think.

You don't HAVE too...  But if you are doing less than 20 mph, you can find a gear in the back that works if you are in the small chain ring for any condition.

If you are in the big ring in the front and hit a hill and drop to less than 10 mph, you will be forced to change the front and the back or you will cross gear and/or get some lovely grinding sounds from your drive train...

Sticking to the small chainring for less than 20mph lets you 'set it and forget it' and you only have to worry about the rear gearing, which, in my opinion shifts faster and easier than the front any day....

Sometimes I get awkward shifts if it's done with more than a moderate amount of power or I'm not paying attention.  I'm running a triple though so there's not as much slack for the RD to take up when I change the front chainring.    The dog fang helps too!

At 50MPH I'm not pedalling at all!  I pedal hard until I spin out and then duck down into the drops in the best aero position I can get cranks parallel to the ground, knees into the top tube, hands on the drops, forearms flat and elbows in.  My chin just clears my stem.  I haven't had the nerve to try this descent in the aerobars yet.

With practice and some good genetics you can get that quite a bit higher, I spin out at 120 currently.  Track sprinters can get to over 150.  But on a descent, gravity, aerodynamics and nerve play the biggest part in top speed.