Some have the custom to wash their hands not only after leaving a cemetery, but also before entering. There is also a custom observed by some to put some water on their face – and not only on their hands – after leaving a cemetery.
It is permissible to smoke a cigarette after leaving a cemetery before washing one's hands.
Strictly speaking, it is permissible to eat or drink in a cemetery, as there is no reason to believe that harmful spiritual forces affect the food or beverage. Nevertheless, it is proper to conduct oneself with a degree of respect and reverence in a cemetery, and one should therefore refrain from eating or drinking. This is the ruling of the Rama (Rav Moshe Isserles, Cracow, Poland, d. 1572). If one wishes to distribute food or beverages to those who visit the cemetery, so they can recite Berachot as a merit for the deceased, he should do so near the entrance, and not in the cemetery. One who recites a Beracha outside the cemetery must ensure to stand at a distance of four Amot or more from a grave, as it is forbidden to recite Berachot near a grave, because this gives the appearance of taunting the deceased who is no longer able to perform Misvot.
When one leaves a cemetery and needs to wash his hands, he must ensure not to take water from somebody's private property – such as a hose in a private yard – which would of course be stealing.