Making big "moves" when shifting can sometimes be a little risky. Anticipation is a good way to avoid that. Fortunately, you can see hills coming, and stuff like that.

Indexed and friction shifters make it easy to skip cogs and stuff like that, but I'd practice a bit before I started jumping around front and rear. After you learn to make smaller shifts smoothly, it's easier to make bigger shifts smoothly.

Early on, "be easy on yourself." That is, keep in a gear you can comfortably handle, because the inevitable missed shift or late shift will come, repeatedly, and you're less likely to be stopped dead in your tracks by any of a few malfunctions that late, desperate shifting can cause. For example, a nice long downhill can have you on the big ring up front, small cog in the rear, but the uphill that follows may beg the complete opposite. What speed you sacrifice by not going whole hog downhill can be gained by keeping momentum going uphill.

The key is to let the gearing do the work, keeping your cadence somewhat steady, which is much easier to say than practice. Until you master this, don't be afraid to spin a little faster on short sections where there is an inevitable uphill grade to follow. Also, don't be afraid to stand and pedal harder if the uphill is short.

Once shifting is second nature, you won't have to worry about that nearly as much.

It'a almost always about momentum. Keep that in mind, and you'll figure out that you don't have to shift to extremes nearly as often.

As far as "The Dancing Chain," it truly is fun to follow an accomplished cyclist on varying terrain and watch the chain moving around while his/her cadence rarely changes. I don't see it nearly as often in group rides (norskagent is an exception, a nimble and practiced shifter), but lately in triathlons, I've been able to watch folks on their tri-bikes working the gears quite often to maintain the higher rpm's that the riding position seems to warrant.