Read the instructions on the home pregnancy test. This should tell you how long you need to wait to get a positive result. Otherwise ask your doctor, he certainly can give you that information.
Usually as soon as the egg have implanted you should receive a positive result on a home pregnancy test. At that point you body has already begun the process of the preparing the body for carrying the baby during pregnancy. The first sign of that is the hormone HCG, that is the hormone that causes a positive reading.
The soonest a home pregnancy test can detect pregnancy is three to five days prior to your the start of your menstrual period. This should occur seven to ten days after implantation.
Generally you will get a positive home pregnancy test the day that your period is late. Check the instructions, some tests can be used earlier, but hormone levels can vary.