When we go to a stillwater we more or less start fishing as soon as we get to the water. Dry fly fishing is immediately different. If we arrive in the morning it may be some time before we start to "fish" simply because there appears to be nothing happening. No flies are out so no fish are rising, sometimes it looks like there is not a fish in the river...
Look in the water. Again in the early season you can gain reassurance that all is well with the river by spotting individual small fry, each of which has already taken charge of its own tiny territory. These troutlets behave just like their full grown counterparts; hanging in the flow, darting up, down and sideways to intercept microscopic organisms even now with all the grace that makes a trout so desirable to us.
This observation is not a waste of your time. It is part of your conditioning. If you are to gain the maximum pleasure from your dry fly fishing I truly believe it helps you if you become so familiar with your surroundings and all that is going on, that you gain the residential status referred to in an earlier post. This relaxed but thorough observation helps you to be more than just a visitor and it gets you ready for when, in an hour or two, the flies will be on the water and the rises will start.
When you do get there early, waste no time, go to the water, walk down river to the place you fancy starting. Get sat down somewhere where you can watch and start taking it all in. This is the start to your approach. Worry not about catching fish. As a resident you will have success anyway, you will see so many more opportunities because of your tuning in, but the bonus is that you will enjoy your dry fly fishing to the utmost and will come again. Next time we will actually start catching fish.
You can practice becoming a resident instead of a mere visitor right now, in the close season, by going for river walks and trying this reconnaissance out for yourself.