Technically - zest is the outer skin of citrus fruits- the pith is the bitter white part under it - between the skin and the fruit. This zest contains volatile oils (flavors) which are lost when dried - so fresh is really best, and probably also cheaper.
You can remove the zest in several ways - with a pairing knife or potato peeler (wide strips), a zester (thin strips), a micro-plane grater or a regular box grater (minced). It depends on what you have and the texture you want. Of course you can always use a pairing knife or potato peeler to get wide strips and then cut them into thin strips and mince them ... this page
will show you the methods to remove the zest. Here is a video on How to Zest
that might help - just scroll down the page and click on Zest Citrus
If I want minced zest - I usually use the plastic wrap on the box grater method ... when done just peel the plastic wrap off and scrape the zest off.
Here is an explanation of Crystallized Ginger
and some substitutes.