Fishing for Browns in the spring is an early morning and late afternoon thing on sunny days. If it's cloudy you can stay a little later, but I've found that the fish shut down around 10am on most days. That's not to say that you can't catch fish all day, but your best bet is early and late. Mid March until about the second week in June are your best months to catch shallow running Browns. After that the thermocline starts to setup and the fish become scattered and start to head for deeper water.
Location is probably the easiest part to handle.
For early Brown Trout action fish the warmest water you can find. Depending on the winter you may be looking for 40 degree water, or like last year in the Oswego harbor, it was 52 degrees. Concentrate off the mouths of tributaries, shorelines, warm water discharges and bays where the water usually warms quicker because of the typically shallow depths. This time of the year I concentrate in the 5-30ft. range, sometimes going out as deep as 50ft. Try looking for mud plumes coming from the tributaries, that water will always be warmer than the surrounding water.