Copper is the most theatrical colourant in ceramics. In an ordinary oxidation firing it gives greens and turquoises; in reduction the same material can give copper reds; in a raku reduction bin it goes metallic. All of that comes from percentages measured in single figures.
Oxide or carbonate
Copper oxide is stronger by weight and coarser, which can give speckling where particles sit; copper carbonate is weaker, finer and gives smoother, more even colour. Recipes name one or the other and the substitution is roughly one and a half parts carbonate for one part oxide, adjusted by testing. Neither is better; they suit different intentions.
Green, turquoise and red
In oxidation, copper gives green in most glazes and turquoise where the glaze is high in sodium. In reduction the same copper can produce the copper reds, which are among the hardest colours in ceramics to fire reliably. In raku, hard reduction in a sealed bin pulls copper towards a metallic lustre. One material, four quite different results, decided by the firing rather than the recipe.
How little is needed
One to three percent gives strong colour; five percent and above tends towards metallic black and can make a glaze run. Because copper is a strong flux as well as a colourant, adding a lot changes the melt as well as the colour, which is why a heavily coppered glaze often runs when the base did not.
Handling and one practical warning
Copper compounds are fine powders and carry the usual weighing precautions. Copper is also volatile at high temperatures and can migrate in a kiln, affecting other pots in the same firing, which is why studios firing copper reds often keep those firings separate. For food-contact questions this site quotes the manufacturer's data sheet and asserts nothing itself.
Questions people ask about copper oxide
What is the difference between copper oxide and copper carbonate?
Oxide is stronger by weight and coarser; carbonate is finer and gives smoother colour. Roughly one and a half parts carbonate replaces one part oxide.
How much copper do I need for green?
One to three percent gives strong green in most oxidation glazes. Above about five percent it tends metallic and can make the glaze run.
Can copper give red?
Yes, in reduction firing, and it is one of the harder colours in ceramics to fire reliably. In raku it gives metallic lustre instead.