If you are using a condom or a diaphragm, there's no lag time, and you can start trying right away (as long as you have been taking a vitamin with folic acid for three months preconceptually !).If you are using an IUD (intrauterine device), once your Ob/Gyn removes the device (a ten second endeavor) you can try to get pregnant right after the next period.
If you are on a birth control pill, finish out the pack and get a period, then just don't restart your pills and contracept that month until you get another period (just so we can better date the pregnancy having had a real period off the pill - not because we are worried about problems if you do happen to get pregnant that cycle), then you can start trying right after that period.
Patients always ask if you have to be off of your pill for three to six months before you try to get pregnant (oldtime advice) - you do not. Even patients who accidentally become pregnant on the pill and don't realize it and keep taking it do not have a significantly increased risk of birth defects and we don't counsel them to terminate the pregnancy.