Ifish, here's the advice I can give you having lived in Leavenworth for 3 years, but only fishing the Icicle about 10 total days. First off it's a beautiful area and well worth the visit dispite very low chances of catching a fish. The river can be floated or fished from shore but bank access is limited. The best spots are just downstream from the hatchery boat launch (get there real early) and by the country club (private) which is about half way between the hatchery and the mouth.
These fish move fast when there in so its ok to find a good drift and just stick with it all day if the crouds are bad. The fish usually come in about mid May but this year the run is at least three weeks late so check the dam counts and make your best guess.
I have only cought 1 fish and I was on eggs and yarn later in the season. All of the other fish I have witnessed caught were on small (about 3") herring or smelt rigged to spin very tightly. These can be purchased at the Safeway in Leavenworth or at Hooked on Toys in Wenatchee (good spot for up to the minute advice). The river is quite fast so you'll need lots of weight. Most guys I see are essentially plunking the smelt or herring in a good hole and waiting for a strike. Every year it seems that there is about a 1 week period where everyone catches a fish but otherwise its pretty slow. I hope you make it when its hot!
Be sure to check out Gustav's or the Leavenworth Brewery for some of the best brews in the state and good luck!!