That's an interesting question and it's a little difficult to answer without knowing what you're starting point is and what your interests are. If you don't have a solid, high school level background then you should start with algebra (often called College Algebra) and some kind of pre-calculus class that includes trigonometry. Once you've got those down, you're ready to get serious with the college level material.
- Calculus I - calculus of two variables, primiarly focused on differentiation with a basic introduction to integration near the end
- Calculus II - more calculus of two variables primarily focused on integration techniques and convergence of series
- Transition to Higher Math - High school gives students the very mistaken impression that math is about solving equations and answering word problems. It would be more accurate to say that it's about proving if and when a solution exists. Actually finding the things is a question for engineers. In other words, math is about developing formal proofs about mathematical structures. This is a huge transition for a lot of students and some degree programs offer a specific class intended to help students make it.
That covers what an aspiring mathematician really needs to know although you could arguably replace the two algebra classes with classes in real analysis.
From here, it really becomes a question of choosing electives. If you already have an interest in computer science, you might consider classes in combinatorics and graph theory. If your interests are more abstract, you could go with number theory a semester or two of topology and add real analysis or abstract algebra if you haven't done both already. If engineering interests you, you could do vector analysis, more differential equations and complex analysis.