Well, hatches and flies will depend on the time of year you plan to fish. I'll stick to winter fishing for now, and we can address other seasons in another post.
You're going to want to fish slowly and deep in the pools that you find. Streamers such as wooly buggers in black, olive and purple all tend to work very well, as well as other streamer variations. I tend to stick with flies tied with some flash to them, but that's not necessary by any means. Same goes with nymphs. Your general nymphs to bring with during the winter will be pheasant tails, hares ears, scuds, midges, ect. Later on towards mid-late February start bringing some BWO emerger and dry patterns, as they will start to hatch if the weather is right. Midges you will find on our streams all year long. My experience has been that you'll want a long(~12') leader in 6-7x for casting those midge dry flies in January in February.
The trout will be very wary this time of year, so moving slow, staying low, and even avoiding bright colored clothes can be very helpful. Bring some split shots to help get those nymphs down as well.
Most days the best bite window will be during the warmest part of the day, as that is when the best hatches will occur.
Also, because Minnesota doesn't have as liberal of regulations as Iowa does, not all trout streams are open during the winter. All hooks must be barbless, so make sure you pinch any barbs on the flies you bring. For a reference on what stream sections are open to fish, refer to Winter stream trout fishing - Trout streams: Minnesota DNR
Which part of Iowa are you traveling from? I can help you narrow down an area to start if you need the help with that.