The mystic works like this....

1. You add an item into the enchantment window/tab (as you would for say, removing a socket).

2. You are provided a list of the current stats you can change, along with a question mark next to it....sort of like....

+ 32-50 Average damage ?
+ 442 Intelligence. ?
+ 446 Vitality. ?
+ 99% Critical hit damage. ?

+ secondary stat. ?
+ secondary stat. ?

3. Clicking on the question mark will show you the options that re-roll attempt could achieve (as well as their appropriate stat ranges).

4. You hit, "enchant".

5. You are presented with 3 options to choose from. These will be the same as you already have and 2 more (which can be the same).

Eg......

I try to re-roll the rubbish average damage to 10% critical hit chance....I get offered

+ 32-50 average damage (ie my original affix)
+ 8.5% critical hit chance
+ 286 armour.

6. I must then choose which one of these 3 affixes I want to keep on the item.

7. I choose 8.5 cc as it's the closest to the stat I want.

I can then attempt to keep re-rolling that stat only the 8.5% cc to get a higher %cc amount. Each time I try this, the material costs remain the same, but the gold cost increases.

note: you can only roll a primary into another primary, and a secondary into another secondary). So there's no changing 1 yard pickup radius for 10% cc ;) also worth noting that on weapons, sockets are PRIMARY affixes

Another thing to note is that as soon as you enchant a rare item, it becomes BoA.

Hope this helps. :)