Fighting in the Coliseum counts as a major action or your job for the week. Starting cash is based on the crowd you draw and generally includes another form of payment, such as money put toward the auction. Starting fights are generally draw around 10 Gp and grow up to 500 Gp purses or more. 5 fights without losing will make you the first arena master.
Fights start out small and become bigger, with the goal of drawing crowds.