This tutorial centers around a useful web based tool called http://keke.itarium.ch/uploads/alchemy/
The URL is http://keke.itarium.ch/uploads/alchemy/
This tool lets you select all the ingredients you own, then gives you a list of the most expensive potions you can brew. As far as I know it's the best alchemy tool out there for making a profit, as it doesn't require you to figure ANYTHING out, like using one of the other tools would force you to do.
Preparation:
For the fastest leveling, you should first follow these steps:
1. Make or buy a full set of the strongest fortify alchemy gear you can get your hands on. Gloves, helmet/circlet, ring, necklace. Wearing these while brewing will make your potions more valuable and stronger, thus leveling you faster.
2. Fast travel back to the original three Guardian stones and equip the thief stone. You can change this back whenever you want. 20% faster alchemy leveling.
3. If you are married, go to your house or spouse's house and wait until late, then wait for them to lie in the bed. Now sleep in the bed to get the "lovers comfort" bonus, which grants an extra 15% leveling speed bonus to all skills.
4. If you aren't married, go to the local inn and spend 10 gold on a bed. Sleep in the bed and you will get the "well rested" bonus which will improve skill leveling speed by 10%
Procedure:
Drop your skyrim into windowed mode and load http://keke.itarium.ch/uploads/alchemy/ up on the right side of your screen. You can shrink the browser window to whatever size you need to be able to see it while skyrim is running.
To start, go to Arcadia in whiterun, and buy all the ingredients that cost less than 100 gold, and all the giants toes if she has them. If you want to wait the 48 hours to respawn the merchant's inventory, do it as many times as you want.
Now alt + tab over to your browser window, select all the ingredients you own, and click the "Show me the most profitable mixtures!" button. alt + tab back into skyrim, Create the top potion, then de-select any ingredients you have used all of, and click show potions again. Do this until Your potions are no longer coming up with a value that you're comfortable with(I stop at about 250), or you run out of ingredients.
Buy all of her ingredients except for daedra heart and void salts(they are uber expensive), Then sell all the potions you made(unless you have some useful ones you want to keep) until she runs out of gold. Now train alchemy with her, and either pickpocket your gold back, or sell more potions. You won't make a profit on your potions by training then selling, but it's a LOT faster than waiting 48 hours every time just to offload some useless potions.
If you want to keep leveling after this, wait 48 hours, buy her ingredients, sell some potions, wait 48 hours, buy her ingredients, sell your potions, and repeat until you run out of potions to sell. Then start brewing again. Don't forget to train with her every time you get a level up.
NOTES:
I recommend de-selecting Daedra Heart in the tool, and not buying it from her, unless you want to buy them to use for things later on such as the atronach forge or Daedric armor. I doubt you will make a profit brewing them into potions if you are buying them. I also usually de-select spriggan sap, as it's kinda rare and has both fortify enchanting and fortify smithing. Blisterwort and snowberries are easy as cake to get, so I hold on to my spriggan sap so I can easily make a fortify smithing or fort enchanting potion when I want.
I haven't had the privilege of doing much using Giant's toes, but Giant's toes utilizing their Fortify Health affect will make potions FAR more profitable than any other ingredient in the game, and thereby level you fastest. For reference, My first run-through with this method, I did not have any giant's toes, but I had nearly every other ingredient. I was missing probably ten ingredients total before starting. I did a grind from 41 to 63 alchemy just as a test of this method, and it took me about 1.5 hours. I did not have the lover's comfort, rested, or well rested blessing, and I was only using two alchemy items - one which fortified by 13%, and one which fortified by 17%


