In order for the government to get a criminal assault conviction in New York State, they have to prove that any injury caused by the defendant was intentional, meaning that it was not accidental. It is necessary to prove that there was an intention by the defendant to cause "physical injury" or "serious physical injury". Both of these terms have a specific meaning in the law; they do not have the general meaning we all use in everyday life.
It may be possible to infer an intention to cause physical harm based on the circumstances of the injury. For example, if a defendant pointed a gun at someone at close range and shot the person in the chest, that might indicate that the intention was to cause physical or serious physical injury, or of course to kill. If the defendant fired a gun several times from close range and missed, one might argue that "missing was the intention" and there was no desire to hurt anyone. On the other hand, firing a shot intentionally, and grazing another person might allow the government to argue a legal theory called "transferred intent". For cerain types of assault charges, it is not necessary to demonstrate that the injury was intentionally caused. Reckless or negligent assaults can be charged too.
An assault charge may become an aggravated assault, if there are certain additional elements. For example, if there is an intent to cause a serious injury to a known police officer or if a deadly weapon is involved, this may be considered aggravated assault. Defenses against charges of assault may include a lack of intent or injury, a claim of justification or self-defense, or consent (like an agreed-to boxing match) although this is inapplicable when it comes to certain types of assault charges.
People who are facing charges of assault might want to talk to an attorney about a criminal defense strategy. For example, eyewitnesses that may be used by the prosecution for identification are often inaccurate, and their eyesight and recollection may be disputed. A common situation is a bar fight, where alcohol may cloud memmories or perception. A person might be able to present their own eyewitnesses to dispute the prosecution's account, or might have evidence they were not at the scene of the crime, also called an alibi defense.
The best advice is to not discuss the case with anyone and call a lawyer immediately.