You increase your alchemy skill, either via enchanted gear, an alchemy potion, or both. I don't know if it still works on newer releases, but it used to be a thing to cheese the crafting system by making an alchemy potion, drink it, make a better alchemy potion, rinse repeat. Then once it's high enough you make powerful smithing and enchanting potions and then use those to craft gear (rings, gloves) to permanently enhance your crafting.
If you're making them yourself, the effect you want is called (for example) "Fortify Smithing". In this case, you can mix a potion containing Glowing Mushroom and Bisterwort (found in caves). You can also check alchemist vendors, they may have "Blacksmith's" potions of various names.
For healing, you want Fortify Restoration followed by a healing spell - though Restore Health might work better depending on your use case. My usual healing potion is Wheat+Blue Mountain Flower, both ingredients really easy to find, and the potion also temporarily increases maximum health.
Thank you so much! I'll try making it. Funny story time, there was a time when I capture all the blue butterflies in Whiterun and Riverdale they did not come back for few days. I needed to raise my potion skills and I don't want to travel different places because I got lazy. So I end up doing the cheese way to get ingredients. By punching the merchants and then resets if they don't have the items what I'm looking for.
Level up your alchemy by making expensive potions and invest points into your alchemy skill tree.
There's also two more ways to increase your numbers:
The legitimate way:
Learn the fortify alchemy enchantment. Use some grand/black soul gems to create a set of armor (I think gauntlets, helmet, and jewelry) with the fortify alchemy enchantment. Brew a fortify enchantment potion while wearing that armor (I highly recommend a mod to increase the potion duration). Drink the potion and enchant a new set of armor. You'll start building up a big buff after a few times of this. You can also brew a potion for smithing for better armor and weapons.
The illegitimate way:
Enchantments are counted as restoration magic. Fortify restoration potions affect the armor enchantment bonuses too. Take a potion and put your armor on and now it's buffed by the potion effects too. There's a bug that allows the bonuses from the potion to persist after the effects should have worn off. A quick lookup shows this:
If your character has an Alchemy level of at least 40, the Benefactor perk in the Alchemy skill tree, and four pieces of armor with at least 8% Fortify Alchemy Enchantments on them
This will allow you to make some insane armor and weapons by abusing this glitch.