For the casino, go to the underworld entrance, then walk toward the ocean following the cliff face west.
You can't miss it.
As for the other side of the underworld, It's a circle with a break in it over the river. Gargoyles can fly back across the broken bridge, when going clockwise, but humans and elves have to find other means. Going counter-clockwise (using the secret door to the bloodworm/blood elemental area) takes you to a teleporter that is one-way, but puts you at the top of the spiral steps to the Abyss (between the Green and Gray goblins). You can't gate there, but you can recall/sacred journey out of the Underworld on regular shards. SP, you got to look for other options (then again, I believe SP has an alternate location for the Underworld entrance, not having Trammel). Continuing counter-clockwise, you can walk out of the underworld to the entrance, by going left through the no-man's land between the two goblin areas (not going into either) across the vine area, then down through the undead area (see next paragraph - there are hidden areas off it), across the bridge, through the bloodworm area, and finally through the acid slug and slime areas back to the entrance. There's also several quests to familiarize yourself along the way, and areas with stealables.
There are several other hidden areas in the underworld. One goes to a landing that is a safe fishing spot, another goes to the experimental gem area, and a third goes to the room with the greater poison elemental, which has a teleport. There's also a teleport past the Gray goblins, prior to the spider area outside Navrey (a boss area that, if you haven't done, you should try - though many shards have a teleport straight to Navrey gotten by an EM goof on one shard being duped). The teleporters, IIRC, lead to a platform maze (that looks broken but can be walked across if you know the path - and there are ways back to the top if you fall off) to get back to the area with the blood elemental and rotworms.
The last option is (if it lets you - you might need a quest), to go down the spiral steps to the Abyss, and either use a teleporter in one of the two houses in the abyss (most shards had, and still have, houses with teleporters installed to the outside), or find one of the two fel-ruleset champ spawns down there, and use one of the sparkly teleports there to get to one of the Fel dungeons, and leave via it.
Note - the hallway puzzle is a bear (though easy if you use one of the guide pages for the puzzle itself), and the goblins of both colors are the primary source for common and uncommon music gears with Stygian Abyss music for Dawn's music box (12 common and 5 uncommon; leather wolves are the only other known source). The SA "rare" gears are actually 10x times easier to get, off all the SA mini-bosses, the volcano elementals in Eodon, and other sources. The experimental gem puzzle requires a good connection and quick reflexes.