The next stop: The Big Horn River
Located south of Billings on the Crow Indian Reservation this river is fed (today) by the Big Horn Reservoir and is fished (usually) from the Yellowtail Dam to the Thirteen Mile access.
Guides are availiable in Hardin, Mt.. Fishing without the benefit of a driftboat or raft will slow down the serious angler. However, a major portion of the raft and driftboat anglers will float to a likely hole and fish by wading until they decide to drift to the next likely spot. There are only a few accesses on the river so you may keep this in mind.
The two major things which have to be brought to mind about this river is:
1. the fish population is probably the number one ranking fishery in the state (rainbows and browns.) Fish reaching twenty inches are not uncommon and on a "usual day" a proficient angler can see several fish of this size come before a camera's lens.
2. The second thing is that The Big Horn River is heavily fished (which has been known to raise some anglers tempers as they search for a "quiet spot." or when they feel invaded by someone, just like themselves, who just wanted to get a line wet.)
Naturally in the summer (particually June) when other boat floating rivers are still at high water the Big Horn is "sold" to many arriving anglers in a big way. Thus the traffic is increased and fishing pressure is turned on. Therefore, keep this in mind... I usually fish this river in the fall (Sept.- Oct.) when the pressure has been greatly reduced and when I don't have to look at what someone else is doing to agrivate me.
Many anglers will fish a fly and dropper on the Big Horn. But caddis small (#14-18) mayflies (tricos), midges and stoneflies are the choice topwater flies. The river also holds scuds (Western fresh water shrimp.) I, myself fish with nymphs almost the whole time that I'm on the river and nymphing is the "preferred" method by many of the more accomplished guides who haunt these waters.
Okay now for some of the realities of the river. Since this river is so heavily fished you may have to be creative with your presented flies. Don't expect that you will just show up and the fish will begin to jump on your line (although I have seen it happen.) Personally I believe this is not a river that can be fished in just one day and have that one day experience satisfy your cravings. Expect to spend a few days on the river therefore a room in Hardin, Mt. may be what you need to book (well in advance) before you think about showing up at the river. A guide also may be beneficial for your opening day on the Big Horn.
The river itself has small gravel on most of its bottom and plenty of green vegatation. Neoprene waders and boots with felt soles are the choice here (since the water from the resevior is cold.) Rod weight should be 4-5-6 and depending on the season be prepared to reduce your tippet material to 2 lb. (just in case.)
The Big Horn is just a few hours from my place so stop in and I'll tell you where the fish are active.
Doc Knoll
I'll get around to telling you something of the other good rivers to fish while you enjoy the Montana landscape this summer. I'm sure Ian will keep the stories steadily.
Introduction > North Fork of the Flathead
Last Year On flyfishing.About.com:
Heidi Land - Montana/Wyoming
Visions of flowering mountain meadows and crystal clear mountain streams with some great flyfishing mixed in. Doc Knoll recommends a visit to this area at least once in your life!
Two Years Ago On flyfishing.About.com:
Consider A Custom Fishing Rod
There are a lot of reasons why a custom rod should be considered by serious anglers. Build it yourself or have a pro do it for you.
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The Muncher is a favorite of Ian James for carp, smallies, more. 
Thoughts of a Chicken Rancher. Doc tells it like it is.