So i'm going to assume if your reading this and you know what stealth is (prowl for druids, but i've never heard a druid refer to it as prowl) so i'm going to go through stealthing, gear, consumables and talents that will help you in your stealth runs.
It's surprising the number of players who think they are good at stealthing, and die horribly trying to get to a boss, i've also seen a number of stealth runs fail miserably because the healer has no stealth talents (feral instinct) and no stealth items so never makes it to a boss. Every death means a delay, depending on the instance, a death run can take 5+ minutes thus slowing the stealth run down by a fair amount.
Stealth increases by 5 points per lvl, at level 70 a player will have 350 stealth points.
Although some instances are easily stealthable without any stealth items, i would say some are probably impossible without stealth items, stealth items such as gear and pots increase your stealth level, and thus decrease the chance mobs will have of detecting you. Here is a list of what can improve your stealth.
Night Elf (Shadowmeld) +5 stealth
If your a Night Elf (which all alliance druids are) you will have +5 to your stealth lvl
Master of Deception (MoD) +3 stealth per point, total 15 ponts
Feral Instinct+5 per point, total 15 points
Enchant Cloak Stealth +5 points
It's quite common for stealthers to enchant a low lvl non BOE, BOP cloak so they can lend it to new stealthers etc
+5 Nightscape Boots
+5 Whisperwalk Boots
+5 The Masters Treads
+5 Silent Strider Knee Boots
+8 Darkmantle boots (Rogue only)
+8 Boots of Displacemement
Trinkets (JC Only)
+3 Figurine - black pearl panther (once upong a time just before TBC was released this was purchasable for about 40s from a vendor, unfortunately now it is JC only)
+5 Figurine - nightseye panther (JC Only)
+8 Stealth of the Stalker
+30 Sneaking Potion
Other items/gear that can greatly assist in stealthrunning
Anything that increases your stealthing speed is of great assistance to speeding up your run, and gives you safety in stealthing away or around pats in the instance.
Fleet Footed or Camoflage, 3% speed increase per talent point topping out at 15% (does not stack with enchants)
Rogues can sprint in stealth
SAP (help you and other members in your group to get past difficult humanoid mobs)
Feral Swiftness - increases speed by 15/30% only when outdoors, since most instances are indoors, it probably won't affect your runs that much Druids can dash in stealth
Soothe Animal - surprisingly this ability which i'm sure the majority of druids finds totally useless, is actually quite helpful to get past difficult to stealth past beasts.
8% Minor Speed
8% Boar's Speed
8% Fleet Footed
8% Swift Starfire Diamond (does not stack with Enchant)
8% Swift Windfire Diamond (does not stack with Enchant)
Goblin Jumper Cables XL - it's always a help if someone dies and you can use jumps on them as an alternative to a druids Battle Res
Goblin Jumper Cables - a lower success rate then the XL version
Gnomish Cloaking Device - great to get past hard spots unfortunately stealth seeing mobs can see through this and when you come out of invis your out of stealth, the CD is 1 hour.
Darkmoon Card Twisting Nether - Collected from the darkmoon fair portals deck, gives you a 10% self rez chance, however make sure you run into a spot you can safely self rez, if you accidently agro
I would say it's advisable for the majority of stealthers to get naked at the start of the instance, even if your a pro stealther yourself an "accident" from one of your stealth buddies could train a bunch of mobs on you, less repair bills = more profit!
Of course rogues confident in their ability to vanish can get by just as well with gear on, but remember vanish has a CD.
There is no need to get entirely naked, just take off the durability items, if your bags are full, just remember that weapons and epics cost more to repair then the lesser quality items, i highly recommend a mod like itemrack, wardrobe or something similiar to easily get changed into your stealthing suit.
Non Dura items are
If you wear higher stam items in these slots, this gives you a chance to be able to die in a safe corner to be rez'd.
If you don't have a pair of stealth boots, it's advisable to get a pair of nightscape boots (these should be quite cheap from the AH) with the minor speed enchant to help you in your runs.