I've noticed that a fair number of visitors to the site are following searches for "wow deadmines" and getting my short report that I actually finished that dungeon. I imagine that doesn't help them a great deal if they're looking for advice, so I thought I'd elaborate a little on my experience. There are spoilers in this article, so don't read it if you want to discover these things for yourself.
As most know, the Deadmines run beneath the village of Moonbrook, which lies southwest of Sentinel Hill in the region of Westfall. The village itself is crawling with Defias rogues and mages, although there are usually enough players working in the area to keep them under control. You should be at least level 18 before you attempt the Deadmines, and you should have a well balanced party to assist you.
You enter the Deadmines through what looks like an old tavern in the southwest corner of the village. You'll find a shaft inside that leads down into the mines proper. You have to maneuver through the tunnels for a while before you find the entrance to the "instance dungeon", at which point only your group will be present. While working your way to the instance, be wary of "elite" monsters that wander this area. These can easily defeat a lone player, and they can wipe out your group if you "pull" too many of them into a fight. The rule of elites is to try to fight one and only one of them at a time; use "crowd control" abilities to keep additional monsters at bay while you bring them down one-by-one.
If you have the "Collecting Memories" quest, you don't actually need to go into the instance: the quest items you need are in the "public" part of the mines. Just look for an area with violet-colored stone on your map.
Once you enter the "instance" most of the monsters you kill will stay dead, but there are patrols that occasionally reappear even if you kill them. You don't want these patrols to fall on your party from behind while you're fighting a tough boss, so check for them before starting a hard fight. A Hunter using the "Track Humanoids" ability can be particularly helpful for detecting patrols.
The first major encounter is with a big ogre. He's apparently immune to a Hunter's "concussive shot" effect, so don't waste energy on it. Let a Warrior get his full attention before your mages start unloading on him; you don't want him beating on a fragile character.
In the Lumber Room, you'll find Lumbermaster Sneed riding in his Shredder. There are several other goblins in the room, and it's both easy and recommended to pull them out and take care of them before engaging the Shredder. The machine is tough and it hits hard. Again, make sure a very durable character (Warrior or Paladin) has its full attention before your spell casters unload on it. Don't relax when the Shredder falls; Sneed himself will jump out and immediately start attacking.
Past the Lumber room, you go down a tunnel to the Smelter, which has a spiral ramp downward. The goblins in there have guns, flame grenades, and little mechanical beasties. An oversized goblin named Gilnid is the boss at the bottom. A patrol apparently starts into the Smelter about the time you defeat Gilnid and open the next door; they seem to be timed to reach the bottom of the ramp about the time you're engaging the guys on the other side of the door. Plan for them!
After that, you're off to the secret construction dock for the Defias pirate ship. Your first major obstacle is Mr. Smite, who guards the boarding plank. Someone tough should hold him off while the rest of your group eliminates his assistants, then everyone can wail on him. He'll use a mass stunning effect twice to delay you while he runs to get a better weapon; it's best not to have his buddies beating on you while you're stunned.
There are a couple more mini-bosses as you work your way up the ship, ending with VanCleef himself at the top. VanCleef can supposedly resurrect his fallen assistants, but he won't if you keep him busy enough (I never saw him try it during my run). Better still, you can just use crowd control techniques to keep his aids out of the way while you concentrate your firepower on VanCleef himself.
That's the quick and dirty on the Deadmines. I hope you find it helpful. Hopefully I'll be able to put together something for Ragefire Chasm in the near future.