Answer:
The requirements for becoming a veterinary technician vary from state to state based upon the laws governing the practice of veterinary medicine and/or veterinary technology. However in many most states where there are actually requirements to be a "veterinary technician" you must be a graduate of an American Veterinary Medical Association accredited college degree program in veterinary technology, have passed the Veterinary Technician National Exam and have passed a state exam.
To find a list of AVMA accredited programs you should go to the AVMA website in the Related Link below. There are more than 150 programs in the US that offer degree programs in veterinary technology. Around 9 of those currently offer approved online degree programs, but you must have either a veterinarian or a credentialed technician as a mentor in order to earn your degree through one of these programs.
For specific information on what is required in each state, the veterinary technician association for that state should be contacted.