There are two kinds of injections -
a subcutaneous (SUB Q) injection (under the skin) and an intramuscular (IM) injection (in the muscle).
To give a SUB Q injection, you pinch and pull up a small piece of skin making a "tent". Use a 1/2" needle to avoid going in one side of the tent and out the other. Inject the medicine or vaccine.
To give an IM injection you place the needle directly into the large muscle in the lower hip (primary site) or the shoulder (secondary site). Again, use a 1/2" needle. To make sure you are in the muscle instead of blood vessel you may want to pull back on the needle plunger a tiny bit to see if you can see any blood in the syringe. If you do, then select another site.