Summarize:

If you quit there was likely a reason. Even if you think your boss was at fault, if you want your job back you will have to submit to them. You need to focus on your own attitude and desires. How can you adapt your attitude to be accepting of a future working in the company you just quit? If you go into a program and successfully complete it, be sure to inform your former employer of your success. This shows maturity and growth. Unless you left for a legitimate reason (e.g., moving away for college), by now you are thinking that something has changed between when you quit and now. Apologize to your previous employer and boss letting them know you regret your decision. That your attitude has changed and you have realized your mistake. If there were hard feelings, ask your employer to forgive your bad behavior and reassure them that you have changed. If they hire your back, they can depend on you long term.  Try to make your apology sincere by doing so in the most thoughtful way possible. Avoid apologizing by text or email. You should apologize face-to-face if possible. By phone if not. If you get their voicemail, ask for a call back or let them know you will call back. Do not apologize by voicemail. In your apology, admit fault and responsibility. Be sincere and let them know you know you made a mistake. If you said anything inappropriate, be sure to note you are sorry about that too. Don't be clever. "I'm sorry, I was wrong" shows strength of character. Anytime you leave a job you should revise your résumé or vitae. Go ahead and do this so you can resubmit it in the future. Take time to polish it so it looks remarkable. You want to show your previous employer you can act professionally. Go ahead and submit your résumé or vitae to your previous employer even if they are not hiring. You may decide to use your internal contacts to forward your résumé or vitae to the right person. When you submit your updated materials, do so widely. Give them to the hiring personnel as well as your former boss. You may want to let other managers you were on good terms with know you are looking for work again. This way you follow the proper procedures by filing with the hiring people and you can get others interested in hiring you. Try to focus on your own change as a person rather than negative aspects of your job. The goal here is to show you are reliable. Even if you were not reliable in the past you can highlight your past mistakes and how you have resolved them. You are more reliable now than before because you resolved your issues. Your boss or employer may be amicable to your return pending some sort of penance. They may accept you back at lower pay or in a different, less desirable position. If you want your job back, accept their conditions but emphasize you want your old job back. Then you can show them how serious you are about reacquiring your old job. This will give you time to re-earn their respect. Don't allow yourself to be demeaned too much. Taking a lower position or a drop in pay is one thing. Being harassed or bad mouthed in the office is different and is unacceptable.
Resolve your own issues first. Apologize to your previous employer and boss if needed. Revise your résumé or curriculum vitae. Submit your updated résumé or vitae to your previous employer. Be prepared to answer questions about why you quit. Humble yourself before your boss.