Sticking the categories in Part I and Part II, what gear helps you sneak? And are there any tactics you can use to augment them?
Sound - How can you move more quietly?
First, some gear.
Moccasins / Tabi / Padded Footwear - From Low-Tech. These light, thin shoes give a +1 to Stealth vs. hearing attempts. Muffled steps means quieter movement, but you trade off some DR - you get all of DR 1 for moccasins and tabi, compared to DR 2 for boots. DR 2 isn't much, but that one point margin can spell the difference between "I pull out the caltrop and keep walking" and "I yell in pain." But 1 point of Stealth can be the difference between getting detected or being too quiet to hear.
GURPS doesn't break boots up into soft or hard like AD&D did. Rather it has three steps - very soft shoes like moccasins and tabi, normal footwear like sandals, shoes, and boots, and noisy footwear - such as hobnailed boots (Low-Tech p. 98). So regular boots are normal Stealth.
Mukluks - a special case - if you need to sneak on snow, mukluks knock off 2 points of stealth penalties in snow. Generally not so useful in a dungeon, though - how often is there snow, and how often do you need to sneak across it? But it's worth knowing they are out there, if you've got a mage with Create Object and an odd patch of snow to sneak across.
Thieves' Mail - From DF1, this armor's weight doesn't count against you for determining encumbrance-based Stealth penalties. That's a good way to get better DR but also to avoid making noise. Thieves' Mail is better than leather for sneaking, and as good as no armor at all. That's seriously good.
Next, some tactics.
Oil locks and doors. It's worth looking to see if the door is a creaky sort before you try to open it. Use oil (not the flaming kind) on the door to let it swing open and shut more easily. Avoid doors that won't open this way until there is no need for stealth.
Another tactic for dealing with doors is to use somewhat quieter ways to bypass them - magically pass through them, use acid on them (watch for smell, though, it's a rare metal-dissolving acid that has no odor), use rust monster slime, whatever. It might not be silent but it's a damn sight quieter than bashing or muscling through.
The Lockmaster spell can substitute for a skilled thief, but nothing in the description says it opens locks quietly. So in my game, I rule they open with the same sound you'd make with a key. It's as quiet as the lock would normally be. It's a one-second works-or-doesn't thing, and that's not slow. A thief can at least try to muffle his sounds a little more in my games, by taking more time to work and s-l-o-w-l-y moving the parts.
Tie down loose stuff. Seriously, you want a bonus to your stealth roll or want to avoid penalties? Don't wear loose clanky stuff.
Move slowly. Stealth is at -5 if you move faster than Move 1. So don't do that.
Obscure your noise with other noise. Time your movements to match louder sounds. If the dungeon has a regular set of noises, try to time your movements to those sounds. Step when the patrol stomps by, take advantage of that distant scream of some unknown victim to move further, and otherwise move only when potential threats have Hearing roll penalties.
Vision - How not to be seen?
This one is tougher. There isn't a lot of low-tech gear to help you see in the dark - you need magic or other supernatural aids for that. A couple things will help you not to be seen, though.
Colored Clothing - In Low-Tech, p. 126. Nothing says you can't substitute Lincoln Green for Dungeon Gray. Done right, this gives a +1 to Camouflage. As LT points out, black is a bad idea, but dark versions work well at night. So dark gray for the dungeon, if it's the stereotypical gray stone walls.
Camouflage Paint - Also in Low-Tech. You know you want to smear grey-and-black stripes on yourself like Arnold. Just do it, and get +1 to Camouflage skill rolls.
I'm not convinced a hunting jacket, with pattern-breaking tassles and attached foliage, is a good idea in a dungeon, so I'm skipping that. It could make you look like a member of the S1W, but that doesn't seem like it'll help in a dungeon.
Tactics are pretty simple.
Stay out of clear lines of sight. Pretty simple. Don't make obvious movements in front of people. Stick to the shadows.
Don't carry a light source and stay away from light sources. This works well for thieves and scouts, even if their group has one. Stay outside the range of their light, so you're in the dark and blend with it as the light attracts attention. Still, it's only making you sneak better, which might not be enough. Everyone seeing the in dark is better - as covered in Part II.
As the DMG noted, there are ways of throwing off smell if your goal is to stop pursuit. If not, though, masking your own human/elven/half-draconian-elemental-tiefling scent is a tricky business. You ideally want to smell like nothing, so you don't attract nasal attention from monsters you otherwise bypass through sneaking and hiding. If you mask your own smell with something stronger (perfume, oil of citronella, animal scents) you might attract attention. Worse, you might smell like prey.
There isn't any real gear to prevent people from smelling you.
Try to smell like the environment. With that in mind, all you really need is some (free) stuff that smells like the locals do. Rub it on, wear it, etc. Eat like the locals and you won't smell different from them. Disguise (Animals) is important, here, and Disguise probably covers this for non-animals, too.
Other stuff - Some assorted tactics worth discussing if your goal is to creep around without being heard, seen, smelled, or otherwise detected.
Distraction - Distractions are an odd issue here. If your goal is to truly sneak, and not been seen or detected at all, distractions are a bit counter-productive. A distraction might help if you get people paying so much attention to one thing they don't notice you. But effectively you're giving up on not alerting them, but instead alerting them to something that isn't you and hoping they'll assume it was nothing and forget it.
So distraction is a risk - it needs to be good enough to draw attention, but not enough to alert anyone. You can't depend on their reaction.
Disguise - Another iffy one - you replace "I sneak in" with "they don't know I'm not supposed to be there." Again, this is good if your goal is penetration but you don't need to get in without anyone knowing you are there. This one is better for fortress-type areas or pseudo-wildernesses (like in D1-3) than in places like a megadungeon where many monsters don't care who you are, just if you're edible or not. So save it for when you've acting like you belong and not for when you need to not seem like you are there at all.
So that is some gear, and some tactics, to help you get around in a dungeon more stealthily. It's not exhaustive - the gear might be, as far as GURPS books are concerned. The tactics certainly aren't. But they might help you keep the goal the goal - if you're trying to get around without being detected at all preferably, and as an intruder/foe/food secondarily, what makes that easier to do?
Overall, sneaking in a dungeon seems pretty hard. Magic helps immensely, some equipment helps, and you can use all your cleverness to help as well. But it's not going to be easy to get in and out to areas undetected. Or even just in. Good luck!
Special Secret Ninja-only Subsection!
Ninja Gear - Why do ninja get all the cool stuff? Because I wrote them and I wanted them to have cool stuff. So there! If you're a ninja, keep reading. If not, sorry, most of these don't work for you - they take some level of Ninja Talent to get the effects I mention. If you think that's unfair, well . . . hyah! Shuriken in your neck!
Dark/Pitch Dark ninja suits - if you want to avoid visual spotting, you need these (and Ninja Talent 1 and 2, respectively). You net out +2 to stealth vs. vision, +1 when moving (doubled for Pitch Dark). These also add to your Invisibility Art skill.
(True story - I briefly considered making these "kuro (黒)" and "makuro (真黒)" to keep with the Japanese-y names of the stuff in the book, but I went with utility over cuteness in that section at least, especially because they"d stick out badly from the rest of the names.)
Quiet/Supremely Quiet ninja suits - as Dark, but for noise. And expensive but good combination is having both - if you're worried about sight, you may as well be worried about sound, too.
If you can lay your hands on it, the Shokosu Gi is Dark and Supremely Quiet and has solid DR, too, which normally isn't a valid combination.