What ways can I change which enchantments the table gives me in Minecraft?

As enchantments offered depend on the enchantment level and the enchantment level depends on the number of active bookshelves, an easy way to change the enchantments offered is to disable bookshelves by placing torches between them and the enchantment table. That way one can still have the entire 'ring' of bookshelves around the table but get lower-level enchantments. Breaking the torches will restore the effect of the bookshelves.

Select an Enchantment level

In addition to more bookshelves giving better enchantments you will also get three new random enchantments every time you enchant something. So if there are three options on a book and you don't like any of them you can pick the cheapest one and then put a new book in and you will have three more random options. This also works for any enchant-able item it does not have to be only on a book. Typically I use books because you can then store the enchantments in case you or someone else would want/need it later.