Some forms of birth control generally have no impact on your fertility at all after you stop them, and thus give you the same odds of conceiving during any given month as women who were not using contraceptives. Condoms certainly don't have any negative impact on your ability to get pregnant! Women who had a coil removed can usually try to get pregnant right away, and the birth control pill wears off pretty soon too. These methods do leave the possibility of having irregular menstrual cycles for a while. Meanwhile, more long-term birth control methods such as depo Provera may take a long while to wear off.
It is a good idea to talk with your doctor about any hopes you have of getting pregnant in the next few years prior to starting the "injectable birth control pill". In some cases, a year or two may be needed for a woman to start ovulating again. What else can you do to increase your chances of conceiving, besides stopping the use of contraception? Women who come off hormonal birth control have even more reason to track their cycle and verify whether they are experiencing ovulation than others. You can use an ovulation calendar, ovulation tests, and look out for your body's natural signs that you are fertile. If you are in doubt, discussing the possible aftermath of your particular birth control method with your doctor is always a good idea. And a general preconception appointment will also give you the chance to discuss prenatal supplements, diet, and other issues.