You can get urine test strips in any local pharmacy (pretty cheap, usually).
Diabetic ketoacidosis is a serious (potentially life-threatening) complication of unregulated diabetes. Lots more information
here, but the basics are: some underlying infection or health issue, cat not eating, not enough insulin and/or high BG => ketones develop. It can progress rapidly from just a trace amount to full-blown DKA requiring vet hospitalization-- very scary, and very $$$.
It doesn't happen every day, but it does happen. It is easy to test for (and much easier to fix/reverse if caught early), and the potential consequences are so severe, it's something you want to be aware of whenever a diabetic cat suddenly goes "off his feed" for any length of time. Anything above "trace" on the urine ketone sticks merits immediate vet attention-- again, it's quite treatable in the early stages.