Egg flies are an essential addition to every early-season fisherman's fly box. Having a few different types of egg patterns is a necessity as water conditions are always variable and fish seem to switch by the hour the type of pattern they prefer. Yarn egg flies and hot melt glue patterns in single and egg clusters should make up the majority of what you carry but a few crystal/estaz eggs is a good idea if you run into some really active fish.
One good point to remember is that regardless of what type of fish you are trying to catch, the eggs you are trying to imitate will change. After eggs are laid in the water they become less colorful, translucent and eventually milky white in color. Depending on the timing of your fishing trip in relation to the "egg drop", color plays a large factor and testing the waters with several patterns is the only real way to figure out what the fish are looking for.
For fly anglers the best time to target fish with egg patterns is when the egg drop is taking place or shortly after. If you watch the water closely as you are traveling the banks you will often be able to see fish as they are constructing redds. When the eggs are being deposited by fish they will often miss the redds (spawning nests) and get swept downstream. In addition to this, deposited eggs are kicked off the beds when the adults cover the redd following the completion of spawning.
When you use egg patterns, try and concentrate your efforts just below riffles or fast runs. You don't want to disrupt any fish that are actively spawning on redds but there's nothing wrong with fishing downstream of redds. Trout will stack up downstream from spawning fish and greedily eat any eggs that drift off the beds. Targeting these fish is a fun way to hook into good numbers of early season trout.