Purely applied statistics are pathetically easy, you just need to literally memorize a bunch of procedures. A lot of psychologists do that, just cramming down words like “normal distribution”or “ANOVA” without so much as a basic understanding of what SPSS does. That’s how NOT to learn statistics.
Now, if you want to understand the math behind statistics, that’s a tall order. Getting a good grip on probability theory requires an understanding of linear algebra, real analysis of several variables, functional analysis, and some basic set theory. Otherwise, you’d be bashing your head in, trying to make sense of what sigma algebra and Borel set means. It’s tough and anybody who is telling you otherwise is lying (or is an idiot).
Last but not least, mastering statistical theory (knowing the math, being able to do the math, and knowing why it’s done so) will take you years. This is by far, the most demanding and difficult part which separates the mathematically illiterate sociologist, the mathematician who just solves the equations and cares not for the statistical model, and the true statistician - a mathematician who knows the mathematical prerequisites, why the models look the way that they do, why it is not enough just for the arithmetic to come out, why the BLUE algorithm works like that. It also requires and understanding of the philosophy of science, the difference between the statistical schools of thought (frequentism, classical probability, bayesian) and how and when to approach certain problems. You would not, for example, want a pure frequentist approach when applying statistical learning to a machine (indeed, Bayes’ theorem has good applications there) and you certainly would not want to rewrite science from a Bayesian point of view the way some authors like Kruschke advocate.
It’s a long journey. It’s math, and then some more.