This is assuming you have defeated Diablo on Hell difficulty. Blizzard should be fixing this right away, but they're not, so far. So instead, only a few players are taking advantage of everyone else with a monopoly on Inferno gear.
Join the act/quest you want on Hell difficulty.
Leave the game.
Click "Public Games" and join the act/quest.
You can now leave the public game and have access to that act/quest until you change it.
It doesn't matter that everything will one shot you and you probably don't do enough damage to kill anything, because while you're dead, Tyreal will kill things for you.
What Wizards have been doing:
Take The Crystal Colonnade waypoint and zone into Gateway to the Crystal Spire. There you will find Leah's ghost, talk to her and it will spawn Aspect of Terror mini-boss who will likely one-shot you. Since Blizzard will continue casting and dealing damage while you're dead, you want to continuously cast Blizzard on yourself, so while you're dead, Blizzard will keep taking away his health. You will die several times doing this before he dies. Once the Aspect of Terror is dead, cross the bridge and zone into The Silver Spire Level 1 where there is another ghost. The mini-boss that spawns here is much easier because unlike Aspect of Terror, Tyreal will solo this mini-boss while you're dead.
Of course, you can skip doing Aspect of Terror because the rez timer becomes time consuming. Just use Teleport with Wormhole glyph to bypass the little creepers that spawn on the bridge, or die and have Tyreal kill them.
You can now have access to Inferno loot and 900+ dps weapons. You may not get a good weapon every time. People who want to cover up this exploit will tell you that only 300 dps weapons drop. Yes they can, but so can 900+ dps weapons. Farm it up!