First, you need a Fortify Alchemy gear set. Basically, just buy Grand Soul Gems with Grand souls and enchant a set of armors/jewelries. Your enchant skill doesn’t matter, but if you have some skill, things will be quicker. If you don’t know Fortify Alchemy, you need to find an item that gives Fortify Alchemy effect, then you need to disenchant that item to learn that effect. Alternatively, you can use the alchemy items you find, just 3 or more would suffice, but it may take a while to find, so enchanting is better.

Next, you need ingredients for Fortify Restoration potion, those are:

• Abecean Longfin
• Cyrodilic Spadetail
• Salt Pile
• Small Antlers
• Small Pearl

(the first three are the easiest to get – the fish can be found is pretty much all rivers and lakes)

You should have at least 20 potions worth of ingredients. If you aren’t skilled at enchanting or alchemy, it will start of slow at first because of low percentages, but, if you keep doing it, soon it’ll start rapidly increasing.

Now, how to make thing work:

1. Wear your Alchemy set
2. Create 1 Fortify Restoration potion (just one), and drink it
3. Go to your inventory, unequip your alchemy items and requip them
4. Create another Fortify Restoration potion (again, just one), and drink it
5. Unequip and reequip your alchemy items.

Repeat this as long as you want, every time you do this (correctly), your alchemy gear stats will increase, and the next fortify restoration potion effect will also increase. After getting a satisfactory increase (entirely up to you, either 850% or 50000%, your choice), create 10 or so fortify restoration potions, so that you can use that on Fortify Smithing/Alchemy gear (use the potion and equip/unequip/reequip your gear).