For GA:You make resume and travel around your university department and apply for different GA positions they have

TA and RA:You have to talk to your department professors if they have any positions or funding for position and there will be one assistantship form that you need to fill.

Note:Process might be little different in different university but the fundamental is same.During my study I got funding for GA on last day when I had to pay fee and was selected for RA from my professor.Let me know if you have any other questions.