This hopefully isn't quite as stupid as the topic sounds; I know the key, and can successfully steal things at need. But no matter how many times I sneak about, I can't seem to increase the skill level, or even register anything like a gain on the skill (the skill progress thing is always 0/100). Is this likely to be a bug or is there any other way I can get the game to register my sneaking?

Incidentally, my version of Morrowind Code Patch (downloaded sometime last year) doesn't have the option to make Sneak a toggled thing. Not sure if this might have any bearing on it.

What's your sneak level? Sneaking successfully is difficult at lowish (under 35) levels especially in town or in daytime. Try sneaking in caves and you should see some results.

Currently 7. But what constitutes a "successful" sneak? Getting the icon to come up and stealing things from NPCs with their backs turned is easy, but I still get no advancement for it.

I don't use sneak much so I hope an expert comes by to clarify but the icon I think means that you're undetected. The problem IIRC is that in order to get advancement you must be in the targets line of sight and remain undetected. This requires a high skill or favorable conditions; cave, invisibility, chameleon, etc.

You don't need to be in their line of sight, but you need to be within their AI radius. (governed by the Alarm setting)

It does take a decent Sneak skill to be functional though. At least 40.

In the vanilla game, advancing Sneak depends on the time that the icon is on while within the AI radius.. At level 7 it shouldn't take very long, only a few seconds to advance the 0/100 scale.

Ummm, no.
With a Sneak skill of 7, you will basically never be able to Sneak long enough to get any real Sneaking done.

It takes around 40 before Sneak becomes affective.

I'm not too fussed about "real sneaking" as such, as my current character's not stealth-based. But I was at least expecting to have got some advancement along the skill bar with the minimal sneaking he has done. If that's not possible with a sneak skill of 7, advancing your sneak is impossible. Would I have to basically try and sneak up behind lots of NPCs until they turned round on me?

You could also do it the clever way and find a decent Sneak trainer, or have a good Chameleon spell. Though I don't like it either that you basically cannot develop a some minor skills _at all_...

You just need some help sneaking. Get some potions or scrolls of invisibility or an enchanted item that gives invisibility or chameleon and go to Balmora. Go in the second floor door to Clagius Clanler’s shop and then down the inner stairs so that you are standing at the base of the stairs. Go invisible and sneak. As long as you can remain invisible, you will advance your sneak skill. I have a ring of CE invisibility and that is how I advance my sneak skill. You can go from 5 to 100.
http://www.uesp.net/wiki/Morrowind:Clagius_Clanler

You've just gotta sneak around in order to raise your sneak skill. Be near people though, otherwise it won't be useful.

To raise your sneak you do not have to steal anything. Just be near someone and press the sneak button. You need the sneak icon to come up. As long as you are within a reasonable distance to the person your sneak skill should go up. A lot easier if you are behind the person. One easy way of getting it up is to be in a building and get a pole or something between you and them so that you cannot see them. just press sneak. The pole or even being right around a corner will help give you cover. Just to make sure open up your character and hover the cursor over the sneak skill to see where you are. Sneak some and check it again. If it has gone up you are in range and doing it right. If not, then you need to be closer to the person.

I remember people talking about setting their character up in a sneak spot, placing a stapler on the sneak key and then go watch TV.

...and I would recommend wearing as little armor as possible especially boots while you try. Getting Nalcarya's diamonds are a good try.
...and unless you have some real ability try training at the South Wall Club. (You did join the thieves guild, didn't you?)

Ok, here's a little help for how to level up your sneak skill without paying to do so:

To level up a skill that is low, you have a much lower success rate so it is harder to use the skill. So, make it easier. Go outside of town instead of sneaking in town where there are plenty of NPCs (and so, plenty of chances of being seen and failing the skill check). This also helps keep you from accidentally trying to initiate a conversation with an NPC while sneaking (bad idea with a low score ) I suggest sneaking up on rats NEAR a city like Balmora or better yet Vivec (kill sewer rats) where you can run to if you need help. If you wander around where there are a small number of rats and sneak CONSTANTLY eventually you will start to see some gains. It will not be fast, tho (no power leveling off of sneak... at least not with my patience)

Another method exists if you can find powerful sneak items. There is at least one that makes it so you would never have to bother leveling your sneak again. I think that it is too powerful IMHO but if you decide to forget the role playing and instead make for an uber-character we can let you know where this (these?) item(s) can be found

ST
ps. save often vardenfell can be a dangerous place

It makes no difference. You could be clanking around in Dwemer armor and it works just the same.

I find a scrib (they aren't aggressive if you don't attack) and try sneaking up behind them. As soon as the sneak icon disappears, then reverse still in sneak mode, until it shows again, then sneak forwards again etc. It's slow at lower levels but gets quicker to improve as your skill improves. Mudcrabs are also quite good targets as they don't attack until you get quite close. Rats are best avoided for training until you are better at it.