Crafting an enchantment table - what's the trick?

the bit that saved me a lot of lapis: the three offers don't change until you actually enchant something. so if it's showing junk for your sword, enchant a book or a stone shovel in the cheap top slot and the list rerolls for the next item. each enchant takes 1 to 3 lapis depending on the slot, so keep a stack in the chest next to it.

The craft itself is easy: book in the top middle, diamond on each side of the middle row with obsidian in the centre, then three obsidian along the bottom. So 2 diamonds, 4 obsidian, 1 book. You need a diamond pickaxe to mine the obsidian though, so that's the real gate. The trick people miss is bookshelves. On its own the table only offers low-level enchants. For level 30 you need 15 bookshelves around it, with exactly one block of air between the table and the shelves. Anything in that gap, even a torch or a carpet, blocks the shelf from counting. Two high in a ring with a gap for the door is the usual layout.