Morality in dialogue systems has raised great attention in research recently. A moral dialogue system could better connect users and enhance conversation engagement by gaining users' trust. In this paper, we propose a framework, MoralDial to train and evaluate moral dialogue systems. In our framework, we first explore the communication mechanisms of morality and resolve expressed morality into four sub-modules. The sub-modules indicate the roadmap for building a moral dialogue system. Based on that, we design a simple yet effective method: constructing moral discussions from Rules of Thumb (RoTs) between simulated specific users and the dialogue system. The constructed discussion consists of expressing, explaining, and revising the moral views in dialogue exchanges, which makes conversational models learn morality well in a natural manner. Furthermore, we propose a novel evaluation method in the framework. We evaluate the multiple aspects of morality by judging the relation between dialogue responses and RoTs in discussions, where the multifaceted nature of morality is particularly considered. Automatic and manual experiments demonstrate that our framework is promising to train and evaluate moral dialogue systems.