"Don't burn your bridges" when quitting a job is standard career advice. Even if you did burn them – you quit without notice, you were chronically late for everything – it's possible you can take a mulligan and get your job back. Asking your old boss won't be comfortable or easy, so think carefully first. Don't put yourself or your boss through this unless you're sure it's the right path for you.
Decide Whether to Ask
If you're not desperate for a job, weigh your options before making the call. If you're unhappy with your current job, are there serious problems? Or is it just the normal discomfort of getting used to a new workplace? Was the decision to quit your old job a mistake, or are you just suffering buyer's remorse? Ask yourself which job will make you happier a couple of years from now.
Then comes the big question: Will they take you back? If you took a scorched-earth approach when you left and told everyone what you thought of your boss, it may not be possible. If you were a flawed employee but there's no personal animosity, it might be doable. Only contact your old employer when you're satisfied it's the right course of action.
Do Some Research
Before giving your old boss a call, research the company, online or by calling your former coworkers. If you find out your position hasn't been filled yet, your boss may be glad you want to come back. If you learn the department has massively downsized, there may be no point to asking. Of course, it wouldn't hurt if your contacts can tell you whether your boss still resents you or if she's feeling forgiving.
Prepare Your Case
Put some thought into how you're going to request your job back. If you left without notice, you'll need to explain why, and convince him you won't do it again. Was your work subpar in some way? You'll have to persuade him that you've fixed your weaknesses.
One inevitable question is why you want to come back. You can try combining this with an explanation of why you left, perhaps you thought the new job would offer better opportunities for advancement, but you just couldn't fit in with the workplace culture.
If you did screw up, an honest apology to your old boss certainly won't hurt.
You'll feel more confident about the approach if you have a back-up plan. Even if your old job is your top choice for your next job, solicit other offers. That way you won't come across as too needy. Competing offers can also make you more desirable to your old employer, or anyone else you interview with.