How do I get charges of domestic violence dropped?
The prosecutor, not the alleged victim of the domestic abuse, makes the call whether to dismiss charges of domestic violence, but may listen to the alleged victim. If the alleged victim asks the prosecutor to dismiss the charges, the prosecutor might do so.
A criminal case has a very significant difference from a civil lawsuit: in a criminal case, the alleged victim is NOT in charge of the case and does not decide whether to bring it, whether to drop or dismiss it, etc. Rather, the prosecutor's office is in charge of the case. That's why these cases are titled "State vs. Defendant's Name," because the "state" or government is the party bringing the case. The alleged victim is only a witness—granted, an important one—generally called the "complaining witness."
This is important because it means that the only person who could voluntarily dismiss or drop the case is the prosecutor. To get the case dismissed, he or she would have to agree to do so. The prosecutor can bring the case regardless of what anyone, including the alleged victim, wants. That said, a significant factor in whether the prosecutor will dismiss is what the alleged victim wants. Prosecutors will often choose to respect the wishes of the victim in this regard. Also, it can be difficult to win a case if the main witness, the victim, will not cooperate. So if the alleged victim wishes the charges dropped, while it's not at all certain that will happen, there is a reasonable chance they will be.
The prosecutor will look to all the factors or circumstances in deciding what to do. The more serious the violence (e.g., the worse the injuries), the less likely they are to dismiss. If there were other witnesses (so the prosecutor does not need to rely on the alleged victim), they are less likely to dismiss. If there is a history of domestic violence complaints, that also makes dismissal less likely. And, of course, if there was any attempt to harass or intimidate the complaining witness into recanting or withdrawing his/her allegations, that would not only cause the case to not be dismissed, but additional charges for the harassment, etc. might well be brought.
Assuming the case is not voluntarily dismissed, the only other way for the charges to be dropped would be if some significant procedural error were committed. For example, arresting someone without reading them their rights, if they then gave a confession which was key; performing an illegal search; etc. If the accused feels that may have been the case, a consultation with a criminal defense attorney, who understands what is and is not proper in this context, is called for.