For me the biggest thing I have to do is force myself to slow down and really relax. The frequencies of city life are different than those of wild forested areas. In order to blend and flow the angler must slow himself down and be in sync with his surroundings. That quote from that English Lord who wrote Complete Angler. "To study is to quiet." Love that.
Job can be stressful at times so I need fly fishing as a relief and therapy. Can't bring "the day" to the water. Must let it go.!!
Now I will usually approach the spot slowly, setting back for a while and watch and listen. Like someone with time to kill. I listen for clicks of reels above or below me, wild life, hikers, etc. Have a belt of scotch, colt, if flies are bad.
Then assemble rod and tie on fly etc. Then I'll stalk up on the spot. Maybe sit again. Observe the in stream, water levels, insects on surface or in air, wind, fish raising, etc. Then when ready, stalk into stream really slowly. Like 10 seconds between each step stalk. and crouch, no big body or arm movements. Try not to stir up the bottom.
I used to use my Teva sandals, with heavy hiking sock, and wade in with nylon quick dry pants. Now I use a pair of water activity sneakers by Salamon on bare feet. They are great. Don't make a big disturbance and are very nimble and light. Have never minded the cold water so don't see the need for waders. Will need a set for spring of season though, still snow on ground then.
Slow down, relax and quiet the mind, is what I have learned.
What is lacked in skill and experience can be made up with patience, discipline and awareness.