Big question, but I'll take a stab:
1) Flies -- small (#18) nymphs. Folks will likely jump in with their latest and greatest, but a good ol' pheasant tail, hare's ear or copper John will catch fish, if you do it right;
2) Tippet/leader -- get a 10 foot 6x leader and some 4 and 6x tippet to replace the tip as you lose it;
3) Strike indicators -- foam footballs are fine. I tend to go as small as I can get away with. Adjust the depth often so the fly is ticking along the bottom;
4) Split shot -- leetle tiny ones about 12 inches up from the fly. You want to sink the fly as quick as you can, but still leave a little life in it;
5) Presentation -- it's imperative to get a natural drift. Flip your fly in well above your target area so the fly can sink down and you can get setup for the drift. Lay the line on the water if you must, or if you're close enough raise the tip to keep line off the water. Using your rod tip, flip or 'mend' the line so that it allows the fly and indicator to float along naturally with the current;
6) Location -- target the seam between fast and slow water. That can occur at the head or tail of a pool, inside a bend, or around any obstacle. These types of locations naturally present problems, because of the conflicting currents, so the mends (#5) are critical;
It's 90 percent presentation and 10 percent tackle. Get a fly that's approximately the size and color of other stuff he's seen float by recently, and you're in. Now all you've got to do is put a fly in the right place, drift it along naturally, and don't do anything to make the trout go: 'What the hell was that?'. Anything between the fly and your feet can mess it up: a crummy drift, splashing the line, flashing rod tip, shadows, clumsy footing.
Good luck.