Your best chances at success are in sports in which you have experience. A degree in exercise science, physiology, or related field helps but is not necessary.
If you have competed at a D1 school it may be possible to start coaching in the program you have competed in; otherwise it would be wise to start one's career looking at Junior college or D3/D2 opportunities. If you are successful at these levels bigger programs will come looking for you.
Pay depends on sport and level. In general, unless you are in a revenue-generating sport, i.e. D1 basketball or football, coaching is a personally rewarding but not usually lucrative career.