Sneaking in adventuring gear, in a dungeon, is hard. Phil Folgio compared it to sneaking with pots strapped to your body, as +Chuck Yelton reminded me.
What if you still want to try it?
Magic will help.
It's been too many years since I played D&D, so all I know there is Invisibility and Silence 15' Radius. I don't know of any spells to help you see in the dark; D&D seemed to imply Infravision meant "see in the dark" in a way that GURPS doesn't. So the trick seemed to be have Continual Light or elves. I'd love to see someone else more familiar with D&D (current, recent, or old-school) post about it and I can link to it in this post.
At least in GURPS, there are a small but useful variety of spells you can use to help you sneak.
Note: I'm going to concentrate here on spells that counteract the detection methods I listed in Part I. I'm skipping spells that either let you "sneak" by some expanded definition of it - by teleporting in, say, or using Body of Shadow to explore, since these often have either serious downsides (can't carry stuff in Body of Shadow form) or serious risks and costs (Teleport, if you even have access to it). For the same reason I'm skipping disguise spells or other things that stop foes from successfully identifying you, but not from spotting you. Otherwise you can get into a too-broad and less useful definition that makes Ignite Fire a "sneaking" spell because you can light fires to distract guards and then sneak in. That's a bit beyond the scope of discussion.
Sound - Your first problem is being heard, since it carries much further than light does around twists and turns. GURPS has nothing quite matching AD&D's Silence 15' Radius, which is a utility spell masquerading as an attack spell.
Here are some ways around making noise, or at least increasing your Stealth score and thus your ability to pad along quietly at Move 1:
Grace - this gives a +1 or more to DX, which is a +1 to all Stealth rolls. It is generally cost-prohibitive (4/4 per level, 1 minute) however, but it's good in a pinch, and useful if you're planning to backstab right after you sneak.
Hush - A good spell, but you can't make sounds when you use it, either. All it gives is a +3 to Stealth or -5 to be heard. So it's a good start but it's not great because you can't speak if you suddenly need to. You can't make a sound. It's potentially useful to silence a guard, though, if you're sure you can beat his Will by enough.
By the way, it's probably simpler to make this spell give you Silence 3, with the limitation that you can't make sounds. Just smooths the rules a bit.
Mage Stealth - Now we're getting somewhere. As hush, but you can make sounds if you want to. This is the version you want, and it's not terribly pricey (3/2, 1 minute). Again, though, the issue is you can still be heard - not well (-5 to hearing, +3 to stealth) but it's possible. You can't pop this spell on and blithely run around the dungeon. Keep sneaking.
Silence and Wall of Silence are useful, too. Silence makes everything in the area quiet - good if you need to keep a group from speaking at all. Wall of Silence is more useful for sneaky camping - you can surround your camp with this spell, and no sounds escape. You can't hear them, either, so you might want to put some kind of visual tripwire or a guard outside of the wall. Neither spell will move around with you, so if you want to actively sneak as opposed to hide, you need Hush or Mage Stealth.
Vision - Vision, not lighting, is the first key. Lighting is bad, because light that lets you see can be seen from very far away. So don't waste time worrying about torches and light spells - it's all the same problem.
You really need to see in the dark to get around without giving away your position.
The Night Vision advantage is useful, but you still need some light to see, even with it maxed out (9 levels). So you can toss the Night Vision spell unless you're in a dungeon lit by its own light sources - torches in a fortified complex, say, or phosphorescent molds or unearthly glowing mushrooms. Night Vision will serve to negate the penalties that come with it, within their radius.
Infravision is helpful, too, but you suffer from only seeing heat patterns - differentiating color, a cold trap trigger from an equally cold normal wall, etc. is going to be a problem. It's not "I see the infrared spectrum and see in darkness as if it was daylight, too" - it's just the heat vision thing. So, equally, Infravision is helpful but not a cure-all.
You really want the Dark Vision spell, although it's somewhat costly (5/2, 1 minute). It's cost-prohibitive for most wizards to keep it on a whole party. Dark Vision will just let you see in darkness, even that of the Blackout spell. It's worth the cost.
One alternative that is easily missed is Sound Vision. Unlike a lot of other "vision" spells that just help you see through material X, this lets you see like a bat or dolphin. You have sonar. It's pricey (5/2, 1 minute), but if your targets don't have ultrasonic hearing, they won't hear you coming, and you can remain in the dark.
But what if you really need to have a light source, and/or can't afford to keep everyone under Dark Vision? If you party has a lot of mages, or can rattle off Mage Sight cheaply and easily, then Mage Light and Continual Mage Light are useful. Only mages can see the light, and thus see by it. So it's good for a party of elves (all have Magery 0), wizards, and folks under Mage Sight. As a plus, the guys under Mage Sight will spot magic items, too. The downside is that while non-mages can't see it, mages can, so "mages, magical creatures, and those under the influence of Mage Sight" are a real threat to you. Don't depend on Mage Light sneaking into the fortress of the Night Elves or the Evil Wizard College.
Their Vision - Okay, now how to we avoid them seeing you?
Invisibility is your go-to spell. It's not cheap (5/3, 1 minute - or 4/2, 1 minute in Dungeon Fantasy), but it works. It's a game-changer in combat, too, which is why DF hits it with a Gygaxian Nerf Bat and says you re-appear if you attack anyone. Its uses are obvious - combine it with sound and smell stealth spells or abilities, and vision in the dark, and you can sneak really well.
Smell - It's all for nothing if they smell you coming. Fortunately, GURPS has an answer.
No Smell: The name is one people goof on, but seriously, it's a great spell. It also serves as a reminder that many monsters will sense you without vision or sound. It won't help against Vibration Sense (Air) very much, but not much will, and against any smell-based opponents all the Invisibility and Mage-Stealth spells in the world won't help if they smell you coming. This helps against guard dogs, rust monsters (if they indeed smell metal), and other sharp-nosed critters.
Other Senses - Magical and unusual detection methods can be fooled, too.
Scryguard - Cheap and long-lasting (3/1, 10 hours), easy to learn (Magery 1 is the only prereq), and cheap to have cast on you in town, Scryguard helps protect against scrying magic - useful if your opponent is using information spells to detect you. Scryfool puts the finger on a decoy, which is good if you personally are being targeted, but generally that's a bit being "sneaking around in a dungeon" territory. It might be valid in your personal enemy's dungeon, though.
False Aura - Kinda cheap and long-lasting (4/2, 10 hours), this one lets you disguise your magical aura as something else. If your opponent is using magical detection to spot, say, the living guy in his armies of zombies, this is a good way to avoid it. In some games, with the right limitations on the Detect advantage and/or the ruling of the GM, it might stop a foe with Detect (Life, Precise) from finding you.
Levitation - Contrary to what my players often insist, this spell doesn't make you silent just because you're making no footfalls. But it will get rid of those footfalls, even if you still make noise (breathing, clanking or rustling, etc.) It's a handy way to deal with noisy footware, and eliminates the noises from climbing obstacles, too. But against creatures that detect via ground vibrations, or who depend on tripwires and noisemakers and nightingale floors to alert them, it's pure gold and should be worth a solid bonus to stealth if not totally eliminating detection. Much the same is with Walk on Air - you make footfalls, sure, but you'll avoid alarm systems.
What about Magic Items? - Some magic items exist that more or less duplicate the above spells. The GURPS Magic system gives a cost to enchant an item under each spell that can be so used. It's a simple enough task to figure out the cost and make of an item that gives you Mage-Stealth or Levitation - or at least lets you cast it. Potions of Invisibility exist, but are pretty expensive compared to the spell.
Some non-magical stealthy gear exists - soft-soled slippers in DF8, some of the ninja suits in DF12, and Thieves' Mail in DF1. I'll discuss these options and some tactics for sneaking in Part III. But generally, the more quietly you want to move through the dungeon, the more magic you need.