I mean you can look up online how to get a Silk enchanted pickaxe.
Nah... just kidding here's a step-by-step guide by capfan67 from Reddit ;)
Silk Touch is one of the enchants you may occasionally see when enchanting tools. Like Fort3, it's slightly rarer than Efficiency and Unbreaking.
It's not necessary to waste picks. The process should be:
Place your pick in the table and check the tier 3 enchant. If it's Silk Touch, then level up and take the enchant.
If it's not Silk Touch, place a trash item, such as a wooden shovel, and use the tier 1 enchant. This will reset all enchants for all items.
Pro tip from Deceptivepiano:
"You can just get the level 1 enchant and then disenchant the item to save levels." "You can do this with grindstone".
Repeat until you have Silk Touch. This may take a number of cycles.