In this sentence, “stream” means a small river. A “trout stream” is a stream where you can find trouts (a species of fish). “Crystal-clear” is a laudative adjective meaning that the river is not polluted or muddy.
“The Cascades and Olympics” stand for a part of the state of Washington, like “Washington's Pacific Coast”. “Cascades” refer to the part of the Cascade Range that is in Washington, and “Olympics” refers to the Olympic Mountains. In both cases, the proper noun is plural because it implicitly refers to a mountain range, which is a set of mountains, so it's plural. “Cascades” is short for “Cascade mountains” (the usual formal name is ”Cascade Range“) and “Olympics” is short for “Olympic mountains” (the usual formal name is ”Olympics Mountains“).
Thus the “crystal-clear trout streams of the Cascades and Olympics” are some rivers located in some specific parts of Washington.
The overall construction of the sentence is “From X to Y, [something about] C”, where C is a category and X and Y are examples of things in this category. This is a fairly common way to phrase this kind of sentence.