You should take it no later than December for enrollment the following Fall. Get three letters of recommendation, preferably from teachers of your advanced mathematics courses. Have transcripts of all previous university courses sent to the university. Of these supported students, the overwhelming majority are TA's. Enough to live on - frugally.
Beginners usually assist a professor who is lecturing to a large freshman class.
Ordinarily, TA's conduct three or four discussion sections per week, help students who ask for it, perhaps grade homework or examinations. Later, TA's have more responsiblity. Typically, the TA's prepare their own lectures and assignments, and may write their own tests. Graduate programs in mathematics want students with strong mathematical talent and the personal qualities needed for success in a demanding field - qualities such as commitment, willingness to work, intellectual curiosity. Letters of recommendation, from those who have taught the student advanced mathematics, are very important indicators of probable success.