Basic Resto-Chugging
This is an exploit that can make weapons that hit for 100,000 damage, and gear that makes you totally invulnerable, or gives you unlimited spellcasting ability.
This method is based on the two techniques above, but is a) based on a program glitch (that could be fixed at any time), and b) makes the game very boring, very fast. I recommend you not use it on a "real" game as it may also corrupt your savefile if you go really nuts with it.
That said, you can oneshot dragons barehanded and perform other miracles at a very early level. Unlike the other two methods, you don't need to prelevel any skills (but it helps) and need very few materials. All you really need in fact are a few dozen mats to make Resto potions, a couple soulgems of any level, and the Fortify Alchemy chant on some junk items.
As noted previously,
most clothing enchantments are considered restoration effects. Enchanted clothing (of any almost any type) will be more powerful if equipped while under the effects of a Fortify Restoration potion.
The exploit involves drinking a Fortify Restoration potion, removing and re-equipping any Fortify Alchemy apparel, creating another Fortify Restoration potion, and repeating the process. Potions will be stronger with each cycle. There is no limit to the strength of potions created this way. In no time at all you'll have potions that boost Resto by hundreds or thousands of times.
Once that's done, its time to make some Fortify Enchanting and Smithing potions. Since Alchemy XP is based on the gold value of potions created, using this exploit will bring you to 100 Alch very quickly. Additionally, Speech can be leveled to 100 by a single sale of a highly valuable potion or upgraded weapon (no matter how little money the shopkeeper actually has), and upgrading a weapon or piece of amor with the aid of a super-powered Fortify Smithing potion or enchantment will immediately max out Smithing.
Extreme Resto-chugging
You can supercharge the spell effects of *any* clothing item without the need to make Alchemy gear or level any skills at all, if you simply have a bunch of crafted Fortify Restoration potions. (If the potions are all the same strength, or are stock Resto potions from a vendor, this trick won't work).
As noted, you need several Resto potions of differing strengths (15%, 20%, 30%, etc). These could come from when you were levelling, or could be made with differing strength Alchemy gear combinations, or from using the Restoration/Clothing exploit previously covered.
For clarity, let's say you have several stacks of these potions... maybe 5 at 15%, 5 at 20% etc. The the stronger they are, the better, but what's more important is that you have a lot of different strengths because the exploit stacks logrithimically.
Look through your Fortify Restoration potions, and drink one from the weakest (cheapest-value) stack. Now drink one from the next-cheapest stack, and then from the next, all the way up to your most powerful (most expensive) stack. (It's easier to look at prices rather than % because the percent values change as you are drinking. ) As you drink each potion, your Fortify Resto will skyrocket.
The only rule: NEVER drink from the same stack twice in a chug-session - it will ruin the session, and you'll have to wait until they expire and start all over again. Just drink once from each stack, from weakest to strongest.
When you've had one potion from each stack, remove all your gear, then immediately put it back on again. Now take a look at the chant strengths on your clothing - they will be significantly higher. I've seen 10% strength items hit 500% in just a few rounds of drinking. 40,000 hp/mana pools anyone?
Note: when the potions time out, the descriptions of enchants on your clothing will go back to their normal values, but the resto-boosted abilities will remain - you can verify this by looking at them under Magic - Powers - Active Effects. They will remain that strong until you remove them.
If you have the mats, it's a good idea to make a few more resto potions at each drinking cycle so you always have differing strengths for next time.
Warnings
Trying to get really high values for item stats can sometimes cause them to become negative numbers. This is called "integer overflow" and happens because of the way computers work. Depending on the item and the severity, it can be really really bad, causing your savegames to become corrupted in a way that might take several days to actually discover.
In short, don't make any gear that shows a negative value!
USKP may have also "fixed" the Falmer helmet thing, I'm not sure -- I stopped using USKP after the team lead decided to start changing game mechanics rather than fix bugs. They are rather arrogant.
head: +30% alchemy
hands: +30% smithing and alchemy
ring: +30% smithing and alchemy
necklace: +30% smithing and alchemy
cheast: +30% smithing
potions: 33% enchanting and 132% smithing
and the armor of ahzidal: +10 enchanting
the pickaxe has no effect anymore
and you forgot to mention the armor of ahzidal with +10 enchanting - tze tze tze ^^