Congratulations for taking on the task of being a part of your diabetic dog's health maintenance team. There are several places on your dog's body where you can easily access a blood supply. I will often recommend that my clients ***** the small vessels are the edge of the ear margin.
Please contact your veterinarian regarding how often he/she wants you to obtain readings. Some people check the sugar level in the urine with simple to use dip sticks. It is not as accurate as the blood test, but it is a heck of a lot easier for repeated spot checks.
I hope that helps...