When a recipe calls for lemon zest, they are meaning the grated peel.

You can use a box grater or a planer.
A planer can also be known as a zester.
A zester or planer  has holes like a gater, but it is small, flat, and has a handle.

To make zest. Just run the planer over the peel to get what you need.

You can also buy dried zest.
That comes in handy if you bake a lot
but you don’t keep limes or lemons handy.

Just remember to cut down the amount if you are using dried by 1/3 to 1/2 the amount of fresh called for. 

If the recipe calls for less than 1 tablespoon zest, you can just leave it out especially if you have juice, or extract in it.
Leaving it out will change the flavor a bit, but not much.
It will still taste good.

Happy A-Z!