How do I enchant in Minecraft PE?

So far, enchantments are not available on the pocket edition. They should be coming out soon, but in the meantime, bookshelves are just pretty for decoration.

You do not enchant at a bookshelf, you would do this at an Enchantment Table, but this is not yet implemented in Minecraft Pocket Edition.

A bookshelf is only used to increase the enchantment level of enchantments when using an Enchanting Table. You can enchant with an enchanting table and some bookshelves, but not vice versa. Villagers (the priest mainly) will enchant your item for a fee of some emeralds as said in the Minecraft Combat Book (Since enchanting is not available, priests will not be able to do this in Minecraft PE. They can only do this in the Full Version).

To craft the table, you need 2 diamonds, 4 obsidian, and a book:

  b            #Formation of Material, b = book, d = diamond, o = obsidian
d o d
o o o

You access the table as if you were accessing the Furnace or Crafting Table. Enchanting Table has not been released even since its latest update to allow day and night in Creative Mode (as of December 2014 - February 2015). I hope this helps you!

There is no such thing as enchantments in minecraft pe 0.11.1 or earlier. It could be implemented later,though.

Actually they will not be coming out with an enchanting table for another year or 2 se they are already making despensers and new mobs like snowman and they are making it able to where you can place Redstone

As of MCPE 0.10.5 on Android, Fire OS, and MCPE 0.10.4 on iOS and Windows Phone, enchantment of weapons, items and armor has not yet been implemented. It will possibly be added in a future update, as the developers gave a list of features that WILL be eventually added to the Pocket Edition, which you can see here, http://minecraft.gamepedia.com/Pocket_Edition_mentioned_features under the 'From the PC version' section of the wiki page.

Have fun playing MCPE! :)