There are 2 spheres that are contending to have infuence over the world - NATO and the Warsaw Pact.
The two spheres are ideologically opposite and are trying to bring nations into their sphere in order to be able to beat the other sphere and attempt to win the cold war, as well as trying to build up support should the cold war go hot.
There are 2 spheres and hence only 2 sphere leaders:
There are several ways of getting into a particular sphere but they all boil down to how good your relations are with both the Sphere leader AND Sphere members.
Bribing a nation within the Sphere that you want to join is a good way to build relations with them. You will then be able to capitalise on these improved relations when it comes to trading and getting treaty's with that nation.
Each time you trade with a nation successfully your relations with them improves, which not only allows you to get treaty's with them easier, but also means that they will give you more money for your products which allows you to make more profit and pay for anything that you need to buy for your nation.
If they like your nation enough to allow you to have treaty's with them, then this is a good way of boosting your relations with them cheaply. Try to get a formal alliance with as many of the sphere members as possible as not only will it provide you with protection, but will also speed up the rate at which you move into that sphere. Being an ally of the sphere leader however will move you much more quickly into that particular sphere.