For almost all areas of math, we want to see real analysis (epsilon-delta proofs, compact sets, Cauchy sequences, etc.) and a theoretical linear algebra course (not just row operations on matrices; there should be linear independence, diagonalization theorems, minimal polynomials). For pure math, a good course in abstract algebra is recommended. For more applied areas, some partial differential equations or complex analysis is good. Generally, the more math, the better. If you are at a school that offers grad courses, then taking a grad course (and doing well) increases your chances. If your school doesn't offer grad courses, then take as many upper-level courses as possible.

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All of our accepted students (except a few who are supported by employers) are offered support by the University, usually in the form of a Teaching Assistantship. This covers your tuition and pays a salary of around $23000 per academic year. This is enough to live on, but you don't get rich. Teaching Assistants teach 4 to 6 hours per week, depending on the course. The total time commitment is around 12 to 15 hour per week. Some more advanced grad students are supported as Research Assistants, with the money usually coming from the advisor's research grant.