The hardest part about developing nuclear weapons is getting access to the fuel, the fissile material. While the methods of doing this have gotten in some ways easier over the decades of the Cold War (e.g. reactors became rather standardized, and centrifuges in particular allowed for considerable "short cuts" to be taken for enrichment of uranium), these are still non-trivially expensive and difficult to implement, and importantly are hard to implement under conditions of secrecy. Most serious attempts at non-proliferation from World War II onward have involved simultaneously trying to keep tabs on the raw materials and facilities needed to process them, while also pressuring states who look like they are engaged in such activities to stop.

Which is to say: the technical aspects are part of it, but the diplomatic aspects are another. The Nuclear Non-Proliferation Treaty (NPT) is of course one of these methods, but has not been the only one employed (bilateral agreements, EURATOM, and just raw pressure have been used by the USA with its allies, for example). Non-nuclear states are given an incentive to join the NPT (they will get "peaceful" technology and can trade such technology with the nuclear-weapons states) and the NPT provides a context for monitoring the use of their nuclear technology ("safeguards") to make sure it is not diverted for military purposes.

The track record of all of these approaches has not been perfect, of course. But monitoring, verification, diplomatic arrangements, occasional threats (which have only worked to discourage allies, not enemies, from proliferating, which is an interesting thing to note, especially in the present climate), control of raw materials (e.g. uranium, which is controlled by the Nuclear Suppliers Group), security arrangements (expanding the "nuclear umbrella"), nuclear basing, and even occasional military strikes (e.g. Israel's raid on the Osirak reactor), have all been deployed.

It should also be noted that the cost and political will itself required to successfully make reliable, deliverable nuclear weapons has apparently discouraged many states from going down that path, even without the other things. Budgets are non-zero games — money you spend on a nuclear weapons program cannot be spent on other things. To make deliverable weapons requires investing not only in the bombs themselves but the rockets, planes, etc., that will get them to their target. It's a non-trivial decision for a state to make; far more states have done speculative studies of what it would require than have actually made them, for political reasons both domestic and international.