In order to test a piece of gold for purity with acid, you need a bottle of 10k, 14k, 18k and 22k testing acid, a rubbing stone and the object to be tested. You can buy an acid test kit that includes 6 bottles of acid for testing gold, silver and platinum and a rubbing stone for around $14.00.
You begin the test by taking the object to be tested and rubbing it on the stone such that the object leaves a 1” long mark approximately ¼” wide on the stone. You then apply a drop of the 10k acid to the mark and watch to see if the mark disappears. If it does, then the object is less than 10k. If the mark remains, then put a drop of 14k acid on a fresh spot on the mark. If it disappears, then the object is less than 14k. If the mark remains, then put a drop of 18k on a fresh spot on the mark. Repeat the process for the 22k acid. If the mark remains when the 22k acid is applied, then the object is greater than 22k.
You will not be able to determine the exact purity of the gold you are testing but you will get an idea of the approximate karat purity.
NOTE: Although The acid test is the least expensive way to test the gold, it is definitely not the safest. The acid is extremely caustic and will burn the skin if it comes in contact with it. Do NOT leave the acid where it is accessible by children.