Straddle her head with her head behind your knees and her body in front. Right near your knee, pull her skin a little away so that it is like a fold in between your 2 fingers, slip the needle into this and give the shot. It is under the skin, known as subcutaneous or subq. If you can get her head into a corner, between your knees, she will be pulling back so that most of her neck is pulling away from your knees, it isn't so hard.
And yes she is probably lonely. Do you have one other cow, or a cow/calf pair that is quiet enough that could "live with her"??? Or maybe a yearling animal? Really she would probably be happier with some cow company, and she will learn to "be a cow" alot faster if she is around another one of her kind.