Safe Digging 101.
The best tip I can give anyone is to become educated about excavating. In other words, understand the resources available to excavators and the legal requirements before digging.

Do you have a pre-excavation checklist? There is an assortment of tasks requiring attention before the excavator should move dirt. Do you know what they are? Most excavators have a pre-excavation checklist which helps organize the excavator and reminds them of items needing attention. If you would like an example of a list see pre-excavation checklist.
Know your one-call law. Each state has its set of one-call specifications. If you are an excavator understand your state's requirements before your project commences. Visit www.call811.com to connect with your desired state's one call requirements.
Call 811 before you dig. Whether you are a contractor digging around a pipeline or a homeowner installing a fence, you must call 811 to have public utilities marked. If there are private services, you are also encouraged to call for a private locate.
Understand your state's tolerance zone and documentation requirements. Each state has its own tolerance zone, an area on both sides of an identified utility. Each state also has its documentation and excavation requirements, particularly when excavating "in the zone." Some require hand digging or hydro or vacuum excavation.