Mabey I'm just being dense but I just can't seem to figure out how to use Alchemy to brew a potion of Fortify Smithing. I obtained several of each ingredient with the fortify smithing effect ( blistewort, glowing mushroom, sabre cat tooth, and spriggan sap). I ate one of each to learn the initial property. Unfortunately I wasn't lucky enough to have the effect I wanted be discovered on any of them, which means I have to unlock the effect the hard way by crafting other types of potions using those ingredients. A little extra work but not enough to ruin my day, so I thought. The trouble is when I went to the wiki look up other potions to craft with my ingredients I discovered that the ONLY property those 4 ingredients share is the fortify smithing. I know you can craft potions using three ingredients but that doesn't seem to help either since only the first two ingredients actually unlock effects.

To further clarify what I'm trying to do here, If I were trying to craft a Fortify Enchantment potion and none of my ingredients gave me the initial property I wanted, I could unlock the effect by using spriggan sap and blue butterfly wing (both of which share the fort enchant effect) to craft a Damage Magika Regen potion. Since none of the ingredients for the smithing potion share a second effect, I can't use that technique.

Is there something about alchemy I'm missing or it it simply impossible for me to make the potion I want?

Blisterwart, Glowing Mushroom, Sabre Cat Tooth, Spriggan Sap.

Try eating those or crafting two of them together.

If you already know the effect, just mix them. You will get the popup telling you that there is a new effect and then the recipe is in the menu to chose.

Select 'Ingredients' at the top left and move to the right. Then select what ingredients you want to mix. You can mix any four ingredients you want that are in your inventory. After you make a potion that does something, it will show on the left and will be highlighted if you have all of the ingredients.

So there is a way to select ingredients to mix without first having the potion available? I'll have to give that a try.

Yep; it's like a trial-and-error way of making potions, which I really enjoy. Also has the side benefit of being able to use up lots of ingredients, thus bringing down encumbrance