How can I copy Items?

First you have to scan a Item with an empty pattern in the scanner to get a pattern with the designated item.
Next you can select the recipe for the item in the replicator and put the pattern in it. As soon as there is enough UU-Matter in it, it will create a copy of your item. (The Re-Inserter that you get with the automation science is desinged to be used with the replicator to make a continious production)

What is the Re-Inserter for?

Factorio does'nt allow a recipe consume count of 0, so your pattern will always end up in the output of the replicator.
The Re-Inserter is basically a Filter inserter that puts its items to where they came from, to put the pattern in the input of the replicator.