Graphene, an amazing two-dimensional material with excellent physical properties, has attracted great attention in various disciplines. Both fundamental studies and applications require graphene samples with controlled parameters including their quality, size, crystallinity, layer number and so on. While graphene can be prepared by direct exfoliation from mother materials or growth on transition metals, the uncontrolled production or the additional complex transfer process has been challenging for graphene applications. Direct preparation on a desired dielectric substrate is an important research direction that potentially addresses these problems. Many advances have been made in the past few years, and this tutorial review provides a brief summary of ways of preparing graphene on dielectric substrates. Various methods including the annealing method, direct chemical vapor deposition graphene synthesis on conventional dielectric substrates and hexagonal boron nitride layers are systematically reviewed and discussed. The main problems and further directions in this field are also presented.