A person can be charged with assault even if they never touch the victim. Most jurisdictions include any attempt to commit a violent injury on another person as assault. Likewise, someone can be charged with simple assault if they touch someone inappropriately even if they did not intend to touch them.
If the actions of one person puts someone else in reasonable fear of bodily harm, the crime of assault can be charged. Spitting on someone or otherwise exposing them to bodily fluids can be considered assault. However, verbal abusing or swearing at another person is not usually considered assault unless the verbal attack includes a threat of violence.