What can I do if I was charged with leaving the scene of an accident but can’t afford a lawyer?

I'm assuming from the tone of your question that you are facing criminal charges.  (This type of allegation can actually be pursued through the civil or criminal courts).  You do need and want an attorney to help.  You may have to wait until your first day in court to apply for a court appointed attorney, but some jurisdictions do have procedures for making this application prior to court.  Call and talk to the court clerk or court coordinator and ask them if there a particular person who handles court appointments.  If this jurisdiction has a person dedicated to handling these matters, then try to get the ball rolling before court.  If they tell you that the judge handles appointments, simply wait until court to make your application for an attorney.  In the mean time, I would still recommend that you try to consult with an attorney or two in your area.  Many offere free or inexpensive consultations.  Get a quote for how much representation will run.  If the judge asks you if you have even tried to hire an attorney, then you will honestly be able to answer yes, give them the names of who you have talked to, and update him on your financial inability.  Some judges get aggravated when people don't even try to hire an attorney before they ask for a free one-- so this will make it look like your effort is sincere.  The other advantage of doing a couple of consults is that it will also give you more info on what to expect regarding your case. 

During your first court appearance, the judge will advise you specifically of what the charges are and ask how you would like to plea.  Tell them you would like to plead "not guilty."  From there, he will either make a decision to appoint you an attorney, or he will give you additional time to find and pay for one.  He may also give you the option of directly talking to the prosecutor.  Many people like this option becasue they feel confident in making their own case--- just keep in mind that if you do talk to the attorney for the state, that anything you tell them could be used against you later.

If this case is a civil case or could be a civil case as well, contact your insurance company.  With certain limits, they can assist you with representation on the civil side of things.