Q:

How do you enchant items with Lapis Lazuli?

I would like to have good enchantments on my armour, weapons, etc. But whenever I put Lapis Lazuli on my equipment, the enchantments never change to what I want! I get more XP and the enchantments change, but they are never helpful!

A:

First, do make sure you have plenty of bookshelves with one air block between them and the enchantment table. A common arrangement is a wall 2 high with 3 sides:

You can use the "torch trick" to re-generate enchantment lists if they are not appealing. 
When you have bookshelves surrounding your enchantment table (with one space between) then the power of available enchantments improves. The list of enchantments is generated based on type of item and number of bookshelves with a single air space between them and the enchantment table.
If there is not an air space between a bookshelf and the table, then that bookshelf does not count. So you can do the following:

Try an item and see list of available enchantments.
Place a torch on the ground so that it is in-between one or two bookshelves and the table.
Look again, the enchantment list will have changed (and will probably offer you something slightly lower level, which can also be useful if you have less than 30 experience)
Try adding another torch to get a bit more variation.

It used to be possible to keep adding and removing torches to re-generate the enchantment lists. When I tried it just now in 1.11_prerelease, this was not happening.
Also, do note for high level enchantments on diamond or gold gear, there is a good chance you will get a secondary effect (not shown at time of selection) or even two. Sometimes by chance this secondary effect is really worth having, although you cannot control or predict it, don't let the "boring" factor of seeing Efficiency IV or Unbreakable III put you off just giving it a try. I ended up with a favourite diamond pickaxe, Efficiency III, Unbreakable II, Fortune II by just taking a chance on this.

A:

You'll need to enchant something to get the offered enchantments to change. Have a selection of items ready to enchant and see what most appeals, or just choose to cheapest so that you can get a new selection to pick from.

