You cannot put fortify enchanting onto your armor in Skyrim.
This is intentional as it prevents a direct feedback loop.
You cannot make a fortify alchemy potion for the same reason.
To clarify, enchanting can boost alchemy, and alchemy can boost enchanting but neither can boost themselves.
gaming.stackexchange.com/users/3917/l I
Yea, as mentioned you cannot created fortify enchanting gear.
You can however, create fortify Alchemy gear, put it on and then create fortify enchanting potions.
gaming.stackexchange.com/users/15558/Nicolai
I have my dragonscale light armor at 744, the boots at that point are 327 (same with gauntlets) and my helmet is 354.
In addition my deadric swords are at 506 each from using the alchemy/enchanting trick.
(It helps to be an orc only because of their perk.)
First you enchant a helmet, gauntlets, ring, and necklace with fortify alchemy.
Then make a potion for fortify enchantments.
After you do this enchant/alchemy loop repeatedly (about three times) the bonuses won't go above 29%.
Finally enchant some armor, a ring, a necklace, and gauntlets with fortify smithing.
Go to a blacksmith station (I prefer Windhelm; if you mess up and need an alchemy table there's one behind the merchants in The White Phial)
drink your potion and make your armor.
Once the smithing is complete I double-enchanted said armor, gauntlets, ring, and necklace with fortify light/heavy armor and fortify one/two handed weapons.
(Pick the right one depending on your character build.)
It is time consuming.
If you know of the chest in Dawnstar next to the mine it sometimes drops grand soul gems.
(Look up Skyrim cheats for more info.
I hope this helps!)
gaming.stackexchange.com/users/19323/rob
You cannot make enchanted gear that would further enhance your ability to enchant for the same reason you cannot make potions to fortify alchemy, as the end result would be instantly having weapons/armor/gear in the millions of percent, and you would lose any value the game had in terms of difficulty.
Yes, this was intentional, to ensure the proper game play experience.
There is no gear you can find within the game that has that ability, and if they did make one (Say through DLC), they would not allow you to disenchant it (Much like certain other items cannot be disenchanted).
Last, there are no ingredients that have an effect that fortifies alchemy, as again, this would result in ridiculous amounts of character skills, making the game way too easy, and could be done easily in the beginning of the game.
gaming.stackexchange.com/users/26043/Damien
Enchant some fortify alchemy gear, then make a fortify restoration potion.
Drink the potion, and re-equip the gear.
Your gear is now slightly more effective.
I.E. 25% turns into 27%.
With this gear still equipped, make another fortify restoration potion.
Drink it, and repeat the cycle until you run out of ingredients.
With this strategy, I made a fortify enchanting potion of 563% bonus.
You can theoretically go on forever.
If you go to far though you will get negative effects so be careful.
gaming.stackexchange.com/users/20284/MCHAMMER
I've been itching to make a set of fortify enchanting gear, but I have yet to find an item with fortify enchanting that I can disenchant.  Where can I find one?  If my only option is checking vendors inventory, can I do anything to increase my chances of finding one?
What disenchantable item has fortify enchanting?
gaming.stackexchange.com
<the-elder-scrolls-5-skyrim>
gaming.stackexchange.com/questions/40939
gaming.stackexchange.com/users/11969/Ryre
You cannot create fortify enchanting gear. It seems that the game mechanics won't allow a player to create gear with fortify enchanting, in order to control undesirable and unbalanced effects.
The community explains that it is impossible to do such a thing.