To apply to the Academy of Veterinary Technician Anesthetists you:

You need to be a licensed veterinary technician and/or a graduate of a veterinary technology program.

You need a minimum of 4500 hours of anesthesia before submitting your application.  That is calculated as 2000 hours of work each year (40 hours/week x 50 weeks/year).  If you provide anesthesia during 75% of your day, that is 1500 hours/year of anesthesia.  You would need a minimum of 3 years to accumulate 4500 hours.
   If you spend 100% of your job providing anesthesia, it is recommended you accumulate three years of experience before applying.

You need to master the required number of advanced anesthesia skills in each area on the skills list and they must be reflected in the cases in your case log.
 

You need a case log of at least 50 (not more than 60) cases you anesthetized between Jan and Dec of the year you apply.  These should be of a variety of ASA ratings (I to V).  They should clearly demonstrate your expertise as an anesthetist.
 

You need to write 4 indepth case reports from that case log that demonstrate your anesthesia skills to their best.
 

You need to submit a minimum of 40 hours of continuing education credits accumulated in the 5 years prior to your application submission.  The CE must be presented by a veterinary diplomat or resident of any American or European College or a VTS and it must relate in some way to anesthesia.