This is what we learned.

Subcutaneous: Pull up skin using your forefinger and thumb into a tent shape. With the longest edge of the needle facing downward, give a quick poke into the skin tent. Draw back on the syringe to make sure you have not hit a vein or artery (you would see blood when you draw back on the syringe if you had). Then slowly and steadily push the plunger to inject the medication.

We bought 3cc syringes with the needles included at our local feed store for $0.35 each. The 3cc's only hold a tiny amount. The needles detach from the syringes.