So, any Demon Hunter Build is going to divide its skills into two basic categories. Tools You Use To Stay Alive, and Tools You Use To Kill Things. In general, these two categories are largely separable, with the former category being the one that changes radically in Inferno. I'll cover both here for completeness sake, but keep in mind that the latter section allows substantially more flexibility.
Staying Alive
There are two schools of thought for staying alive. The first is built on maximizing Smoke Screen uptime at all costs, through the use of the Lingering Fog rune, Preparation with either Focused Mind or Backup Plan (to taste). Multishot with Suppression Fire, as are the Nightstalker, Perfectionist, and Sharpshooter passive skills. These builds have become somewhat less popular after the most recent round of hot fixes, as the maximum possible uptime has been reduced considerably, but Smoke Screen is still an essential element of most builds, regardless. Since the most recent hot fix, you may also consider replacing it with Shadow Power with the Gloom rune. You'll experience a higher uptime of less damage reduction (-65%, rather than -100%). If you go the Shadow Power route, you'll probably want to focus on offensive skills that provide more health regen (see below for options there).
The other school of thought is to maximize your kiting ability. While Smoke Screen is still essential to most of these builds, they may forego some of the other +Discipline stacking options in favor of abilities like Caltrops and Vault, particularly in combination with the Tumble rune, which makes it near-spammable.
Either way, the key is to select skills that maximize your ability to not be hit. Whether you do this by increasing your invulnerability uptime, or by augmenting your mobility is up to you.
Killing Things
On this front, you have much more flexibility. Elemental Arrow is incredibly popular as a main attack. At a cost of only 10 Hatred, you can almost spam this exclusively in most encounters - Hatred builders aren't often needed, (especially if you use the Bat Companion, see below) which means that you can rely on this skill primarily for damage. The two most popular runes are going to be Frost Arrow, which offers high single target damage, decent AE, and a snare effect, and Nether Tentacles, which offers the best damage on single-target encounters, as well as a decent life-leech effect. Screaming Skull is favored by more kite-centric builds, as the fear effect offers a tremendous amount of crowd control - it's not as reliable as some other options, but it's potency and spammability more than makes up for it.
Rapid Fire is also quite popular, particularly with the High Velocity or Bombardment runes.
Hatred builders, by contrast, are much more to taste.
Evasive Fire is a very popular Hatred builder, but the risk of spending Discipline by vaulting unexpectedly is often enough to make it less useful than the alternatives - especially when action bar slots are scarce after stacking Defensive skills. Additionally, the damage isn't terribly high, and it offers a minimal AoE coverage or additional utility.
Entangling Shot is probably the most popular alternative, as the slow is handy, though the damage is pretty lackluster. Bola Shot and Hungering Arrow have proponents as well. This slot on your bars in particular, is largely going to be to taste.
And Then What?
At this point, you have a Hatred-Spending attack, a Hatred-Generating Attack, and probably 2-3 skills allocated to defense. (Smoke Screen or Shadow Power, and some combination of Prep, Vault and Caltrops). You can fit 1-2 more skills on your bar. What do you take? There are a few major contenders:
Companion, probably with the Bat rune - this is an easy attention-free source of additional damage. More importantly however, by generating 3-hatred per second, it allows you to use Elemental Arrow 5 more times (or get 5 more ticks of Rapid Fire), give or take, before running out of Hatred. That's a Really Big Deal, and a lot of extra damage, before even factoring in the 45% Weapon Damage that the bat does on it's own.
Marked for Death, particularly with the Death Toll rune is popular for Shadow Power and Nether Tentacles based builds for maximizing health regen. It's less useful if you're doing a lot of kiting, or concerned with AE damage. It's also very potent in combination with Nether Tentacles -- especially in 'true' single target (i.e. only one thing on the screen to hit) situations.
Multishot with Suppression Fire, as mentioned above, is a popular option for maximizing Discipline Regen. Alternately, with the Fire At Will rune, it becomes a popular AE option for builds that are more focused on single target damage with other skill choices (i.e. (Rapid Fire)
Spike Trap, particularly with the Scatter rune is popular for kite-centric builds - dropping one at a tight choke point can be devastating.
Passives
The only really important one here is Archery, which, in combination with a 2H Bow or Crossbow, is a massive increase in damage. If you're stuck using a Hand Crossbow, this is less important, but you should really be trying to get your hands on a two handed ranged weapon as soon as possible in order to use this passive. It provides an absolutely staggering amount of additional DPS.
Beyond that, it's largely to taste. If you're focused on SS/SP uptime, you'll want some combination of Night Stalker (possibly with Sharpshooter to support it), Perfectionist, and Vengeance. A kiting focused build may want Cull the Weak or Tactical Advantage. You have a lot of flexibility here.
Best Answer
I defeated Diablo as a L51 Demon Hunter last night, it was a tricky kill, as you correctly point out the Shadow Realm is one of the harder parts due to the lack of health restore points. Unlike some of my answers which are based on second hand knowledge, this is direct experience. Your milage may vary :)
Here is my general build and strategy, I have tried many other things that did not work well.
The key factors here are slowing Diablo down, avoiding damage yourself and finding ways to recover health as you go.
I'm using dexterity to help with damage (943% increase due to dex), 2k armor and 4k dps overall with bonuses included.
Slowing
For my primary damage dealing I chose to use rapid fire with web shot. This skill plays well with +Life on Hit and with Life Steal. Also having some +Hatred Regeneration equipment helped keep this going as long as possible. I also use a Raven Companion for a little supplementary damage and regeneration.
I chose entangling shot due to its hatred regeneration. You can choose to use the heavy burden rune to increase the slowing time as I did or you can use justice is served to recover hatred more quickly and switch back to rapid fire.
Avoiding Damage
It should be needless to say but you should be kiting quite handily by A4 NM. In order to keep kiting Diablo you need to slow him down.
I've been using a shield to help bump my armor numbers up but the block and dodge bonuses I received were really the saving grace. I have around 100 fire/lightning resist and around 50 in the rest (not astronomical numbers but every bit is helping). I found that in the main world fights that the lightning/fire burst could quickly drop me but it was usually his circle of fire that hit me hard. To avoid these sudden situations I found that Vault with the Rattling Roll rune was invaluable. Not only could I survive at close range until an attack was imminent, but I could leap directly towards Diablo and add some stun in. I also used this to avoid the bone cages. If I found that I needed to run, I could easily follow up with a Smoke Screen with the Lingering Fog rune after he shook off stun.
In the Shadow Realm I found that if I waited until my clone was just spawning and hit Smoke Screen I could usually wipe him out with Rapid Fire, hit Smoke Screen again, collect the health globe and reposition for Shadow Diablo very effectively. Oddly I found my clone dealt far more damage than Shadow Diablo, especially when being effective at kiting.
Recovering Health
For the shadow realm this is tricky. As I pointed out above, you can use vault with stunning and smoke screen to get you to the dropped health globes, if you have any equipment buffing the health bonus from that, great. I have a base of about 12,000 hp to work with, and I use +Life on Hit (~100) and some %Damage to Life (3%) to keep myself going. I also regenerate about 100 Life/Second. With this setup I can run away, heal a little, throw some quick shots in and slowly heal myself back up.
I also made sure to equip some resplendent health potions (6500 life). Some times that extra 2k kick over heroic potions made the difference. For emergencies I also kept Preparation with Battle Scars available, a missed vault or smoke screen with low health can be fatal. When I started scrambling away I'd rather hit vault a couple of times, preparation and then smoke screen to get out of harm's way.
I used the Cull the Weak, Sharpshooter and Archery passive skills to add some kick my attacks and the were noticeably helpful.
Using this setup it took me 2 tries to kill Diablo and the 2nd try went very smoothly.