It may sound silly to say, but reading water on a small stream is the same as on larger ones, except everything is smaller & more close in to you. Pools, runs, etc will be smaller, but so will your target area for your line & where the trout are holding. You'll have less time & less area to get your line drifting exactly as you want over the fish.
Another problem is that on some smaller waters, trout tend to pile up in greater numbers in the same location. They might not be as spread out as on larger rivers. Since the trout have less optimum places for food & shelter on smaller streams, it's a good chance that where you find one, there will be another. Trout aren't schooling fish, but many times they cluster together at the fewer decent spots that small streams offer. The trick here is to not frighten all of them when you hook into the first trout.
Because of this, you might find trout hiding in places you wouldn't normally consider. Every under-cut in the bank, every brush or root sticking out into the water (even shallow water) becomes a potential place to find trout. I wouldn't pass up any stretch of broken water or riffles on a small stream either. With such fewer good places along a small stream, trout will take whatever cover they can get.
The trout will sometimes hold out longer on smaller waters through the season. However, certain conditions have to be in place for this to happen. A heat wave can be devastating to trout in these streams. So when fishing later in the summer season, choose streams that have a lot of trees covering it, deep pools, & especially the places downstream of where a natural spring enters the creek.
Wading in & around small streams can be dangerous, if you don't know the area. Many of those that run through pastures have steep banks. The ground may not always be stable around the bank, so never stand on the edge. It could be a long way down to a hard, wet landing. Streams flowing through swamps & wetlands may very well have places of quicksand. Getting stuck in quicksand is no joking matter. I know anglers who have & they'll tell you how scary it is. More than a few anglers have died in quicksand, so please, be careful of it. Simple mud in & along the stream can be a problem too. Many times it's very deep & thick along small streams & it's depth can be deceiving. Try one foot at a time & always remember to leave yourself a way out.
Of course, you're fishing in tighter quarters, so you have to be careful not to spook the fish. Every move you make will be magnified & easily noticed by the trout. Go slowly, keep a low profile, & try not to kick out rocks or make a lot of noise with your feet. Quietly & gently shifting your feet to move around is the way to go here. So what if it takes a little longer to get into position?
Lastly, always bring a good working flashlight with you, especially to those streams that flow through the woods. After a fun day of fishing, you don't really want getting back to your vehicle in one piece before they send the search party for you to have been the biggest challenge of the day!!!