A larger river is just a whole bunch of small streams running together. It will take some experience before you learn to see and fish them ALL. But you should be able to walk the bank and find a FEW already. Fish those to start with. Fish them the same way you would the small streams you are familiar with. Deeper water is just fished...well...deeper when using sub-surface flies. Faster water must be fished with a mind to getting your flies deeper faster and keeping them down (more weight, sink-tip fly lines, more absorbant materials, bigger flies made of more absorbant materials, more directly upstream casts, casting further upstream of the water you actually want to fish, and the tuck cast are all various tools for achieving this). When fishing the surface, you must pay attention: keep slack out and tension off your line. Things just happen faster. So the timing is a bit different. But you will adjust quickly enough. Eat the elephant in small bites. Don't spend too much time standing in one spot. Don't be afraid to cover more water more quickly using streamers or other wet flies on a down-and-across swing presentation (especially with a sink-tip line in the deeper portions). You're not trying to catch EVERY fish in a big river every time out. Small streams are approached far more delicately and methodically...as a general rule because you are more visible to more wary fish and you only get one chance per "fishy" spot and you may have to move pretty far to find another one. Not so on most larger streams. You already made the first few good observations and adjustments: dump the non-angler and give yourself some time to focus, take the bigger tackle, and go back and try again.

FYI, most big water anglers are intimidated by small water, too. So don't feel bad at all.