Summarize:

You may need to adjust the needle a bit to make sure it’s inserted correctly. You’ll know it’s in the right spot when you see the blood start to flow.  As an alternative, you can use a vacutainer needle and hub, if you plan to use vacutainers. Your needle should still be about 1.5 in (3.8 cm) long.  You can get a needle from your vet, a medical supply store, or online. If the blood spurts or shoots out, remove the needle, because you’ve entered the carotid artery. As you pull out the needle, place a piece of gauze or your finger over the wound for at least 1 minute. Then, check to see if the bleeding has stopped. Continue to apply pressure until you don't see any more bleeding. Slide the pump back slowly as the blood flows into the syringe. Stop when the syringe is full of blood.  Break the seal before you insert the syringe into the horse’s vein. Don’t press down on the plunger. Stabilize the needle, then use your dominant hand to gently push the vacutainer onto the syringe. Once it’s attached, blood will fill the vacutainer.  A vacutainer is a tube that’s used to collect blood. You can find them at a vet supply store, a drug store, or online. It’s okay to use vacutainers made for humans.  If you want to take several samples, simply remove the full vacutainer and insert a new one.
Insert a 20-gauge x 1.5 in (3.8 cm) needle at a 20° angle. Pull back the pump on the syringe to take your blood draw. Attach a vacutainer to the syringe hub, if you’re using one.