There’s a lot of random rules, but here are some highlights:
New states can be formed, but not within an existing state, or by joining 2 or more existing states or parts of existing states, without approval from the legislatures of those states as well as of Congress.
Constitutional Amendments can be proposed by ⅔ of Congress, or at a convention called by ⅔ of state legislatures (that’s 34). To ratify an Amendment, ¾ of state legislatures or conventions (38) are needed. Congress can choose between using legislatures or conventions to ratify.
You can’t impose a religious test in order to hold office in the U.S.