Contractarianism is an interesting philosophy in that it doesn't present defined "rules" that one must follow in order to be moral. Rather, it argues that every agent has their own internal moral calculus and operates upon their own understanding on what is right or wrong. Given that agents still want to work together out of self interest, they must establish a system of moral contracts that allow agents to respect each others' respective moral calculi.
The syllogism of the framework typically starts by justifying moral internalism, the idea that moral properties are not divine or externally defined but come from within us. This internalism is the reason why agents do not have consensus whether actions are moral or not in the real world – because there is no clear externally defined metric as to what is moral or not. Instead, agents look within themselves.
After justifying moral internalism, the conclusion is that justifies following contractarianism. Since each agent operates upon their own account of morality, but still want to take the "right action," it is important to not impede upon other agents' attempt to be right. By establishing a system of contracts, or rules, we can prevent interference by appealing to each individual's self-interest.
Importantly, contracts must be established in a fair and equitable way. That is, agents must be on the same "playing field" when creating the conflict, as if there is any coercion involved, it would not be valid. Additionally, upholding and following these contracts is of the utmost importance.
This framework is often tricky and can be easily used to trigger skepticism. Even if contractarianism fails but moral internalism is won, that would mean each agent operates under their own account of the good, but now, there is no way to reconcile these individual accounts of morality. Therefore, without a unified system of morality, it could not exist, and skepticism would be triggered.