This isn't a true hike per se, but if you want to explore a glacier without having to rent a guide and be attached to someone with a rope, this is the place.
What can I say? It's a really cool thing to do and it should be a definite stop on your way to or back from the Wrangells, Valdez, McCarthy, etc. The photographic opportunities are endless.
Access to the glacier is only available via private property. Current prices (as of March 2019) per person are $30 for self-guided access in the summer, and $100 for guided access in the winter. For more information, check the Matanuska Glacier Adventures website.
Depending on how far onto the glacier you plan to hike, it may be useful to bring some kind of pole or walking stick, as well as ice cleats.
There is a campground in the area but it's not as attractive as you'd think.
Before you head down, have lunch in the rest stop just before the turnoff. You'll catch a gorgeous view of the glacier and the valley. The campground is an excellent locale but spots can fill up quickly in the summer months.
If you'd like to educate yourself about glaciers and their awesome power, please visit All About Glaciers, a great introductory website.
Take the Glenn Highway just past the Matanuska Glacier Rest Stop (about mile 100). You will see a small grocery store on your right with a road just after it. Take a right on that road and head down into the valley. It is rough and steep and a bit harrowing but otherwise fine. Continue across the valley and over the bridge. A little ways from the bridge you will see a store. Get your tickets there and continue down the road to the trailhead.