Mizzely pretty much summed it up. Birds, zebra finches especially, are hardwired to breed, and there is no 100% way to stop them breeding, but you can stop the eggs hatching by boiling them or replacing them with dummy eggs as soon as possible after they're laid. Removing potential nesting spots, nesting materials and keeping a watch on the amount of protein they're getting (don't remove protein completely because they do need it, but don't offer any extra) can help discourage them. Even solitary finches, which are generally stressed and unhappy birds, may still try breed, such as male finches making nests or females laying infertile eggs. A healthy diet and offering a source of calcium that the hen can self regulate (eg crushed oyster shells, calcium blocks, ect) will help prevent deficiencies and reduce the risks of health problems.