I am just curious how exactly do independence referendums work.
For instance let us assume that some people meet the criteria for a referendum and want to make a non-binding referendum. If they go the United Nations to declare a binding referendum, then if it is accepted, and the results of the vote are in favor of secession. Does the country have to abide by the results or can they just ignore it?
In short, the UN has nothing to do with referendums. A group of people can't "go to the UN and declare a binding referendum".
A country can choose to run a referendum, which may be binding or not according to its own constitutional arrangements. Other countries may choose to recognise a region as an independent country (or not). The UN only expresses the general will of the international community (especially as expressed through the permanent members of the security council)
A region may organise a vote on independence in their region, but there is absolutely no rule or international law that says that the national government is bound by it. There is a general principle of a "right to participate in government" and "the will of the people is the basis of authority for a government". Yet this does not mean that a local referendum is binding, nor that a state is obliged to hold referendums.
To take the particular case of Catalonia. There has been no recognition of the validity of the referendum by Spain. The UN is not directly involved.
If an independence group wants to hold a binding referendum, and the national government says "no" there is no way that the local group can force the national government to change its mind. There is no priniciple of international law that can compel a state to offer a binding referendum on any matter. The UN is not some kind of "super government".
Independence referendums may work in one of three ways:
The country may decide to split, and a nationwide referendum is held by the government to approve this in accordance with the country's constitution. The constitution then binds the governement to the result of the referendum. (Eg the independence of Czech and Slovakia)
The government, agrees to local demands to a referendum and voluntarily agrees to be bound by its result. The national government passes laws authorising the referendum. (Eg the Scottish referendum)
A local government or group decides to hold a referendum without the approval of the national government. Such a referendum may be considered illegal by the national government. (Eg Catalonia)
