A bad conduct discharge is a dishonorable discharge or a "general discharge under other than honorable circumstances." Generally speaking, this sort of discharge means that you did something wrong to get kicked out of the armed forces, and it may have involved criminal charges or conviction. Getting a new job after this kind of discharge can be difficult, but if you think through your options and present yourself properly, you can still get new employment.
Find out the exact wording of your discharge. If you have a general discharge or general under honorable conditions, you don't have anything to worry about. It's only when you have a documented dishonorable or general under other than honorable conditions discharge that you need to take steps.
Attempt to have your discharge upgraded. You can contact the discharge review board for your branch of service and ask them to review your discharge. Unless you have some mitigating factor that you feel wasn't taken into consideration though, you're stuck with a dishonorable discharge.
Be honest with your potential employer about your discharge. If you were court martialed or had criminal convictions during your time in the military, say so on your application. List out the justifications and explain the facts of what happened. If your employer finds out that you weren't honest on the application, you can be rejected out of hand.
It's important to show that you've taken steps to change your bad conduct. For instance, if you had drug charges, then show that you've gone through rehabilitation. It may also be a good idea to volunteer with an organization, such as a local not-for-profit that educates kids about drugs.
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