You should learn calculus and differential equations, and then some probability. At that point you should learn a bit of measure theory and then stochastic calculus builds on all that. Stochastic calculus is basically just weird calculus. It has an additional differential dW and the chain rule is more complex (for the Ito formulation. Stratonovich is different but not by much)

From there you study the behavior of various forms of stochastic differential equations that are intended to model certain situations. Then, you make this cool connection between stochastic differential equations and ordinary differential equations that describe the evolution of the corresponding probability distributions. There’s lots of other stuff but those are the hits.