Getting to this position may require getting well out into the lake so that the sun is behind you. A good quality pair of polaroid glasses is also critical as these allow one to see through the surface tension. It is a good idea to get some practice in when wanting to target fish at the stream mouths rather than getting straight into "hunting mode".
Most times brown trout tend to be stationary in the water and can look similar to a patch of weed or a branch, sometimes just a long, dark patch on the bottom, so it pays to treat everything as a potential trout and to cast to it.
I suggest that 10 to 20 casts per sighting is enough to figure out if what you see is actually a trout or not. More often than not browns are found as individual fish during the hot summer months although they can be in groups from time to time. They may just be within metres of each other so spooking one fish can spook several others at the same time.
If there is any current in the area that you are stalking through try to walk up the current as any sediment that you disturb from the lake bed is likely to put any fish there on high alert, if not actually spook them. It is a little different when stalking trout in our smaller streams though. Most of the very brief sightings that you make are caused by your own movement, particularly a pointing action when trying to show someone else where a fish is.
I like to use bushes or long grass as cover and to only turn my head slowly to scan as much of the area in front of me. Carrying your rod facing forward is a sure way of spooking any fish in the area as well. Learning to "look" through the water is also very important as our eyes tend to automatically focus on the top of the water rather than on the bottom of the lake or stream. Time spent learning this habit is never a wasted exercise.