Zambians follow a strict patriarchal society within Zambian culture — men are afforded more respect than women, and older men are respected more than younger men. However, you might find that a white person, of any gender or age, is granted the most respect of all.
A holdover from colonial times, this might make a traveller uncomfortable, but this is largely a Zambian's way of being courteous. Accept their hospitality.
Zambians are curious people. To a Western mindset, this might be interpreted as unnecessarily staring at you or talking about you in front of you. Be prepared to be greeted by kids yelling mzungu, mzungu! (literally, white man) and answer lots of questions about yourself.
Zambians love to shake hands, and you should oblige them. However, Zambians often like to hold hands for the duration of a conversation. This should not be interpreted as anything sexual; they are merely trying to "connect" with you. If you feel uncomfortable, simply pull your hand away.
If you wish to be courteous or show respect then holding your right wrist or elbow with your left hand as you shake is acceptable. Do not expect a firm handshake as this is considered aggressive, likewise, do not be too firm in yours.
Eye contact is also considered aggressive and disrespectful, you can make eye contact but do not hold it, slide your eyes away, but do not face away.
Women should not wear shorts or mini-skirts, especially as they travel away from Lusaka. (Thighs, to Zambian men, are huge turn-ons.) Low-cut tops, however, while discouraged, are not nearly as provocative.
Pointing with the index finger should not be done, it is considered vulgar.
Finally, when meeting a Zambian - even to ask a question - you should always say hello and ask how they are. Properly greeting a Zambian is very important. They are uncomfortable with the Western notion of simply "getting to the point." Enquiries about children are generally welcome and are a good way to break the ice.