Well, the method I was taught is to be used and is to be successful only when the horse is ready. At first, the horse has to respond to lower his head. Then, the ground is tapped with the crop, and light taps are applied to his lower legs, to encourage to paw the ground. From here, the horse should grasp the feeling that he has to lie down. Additinally, the body language of the human is downwards, too - looking on the ground, hands low, etc. When the horse gets the right feeling, he lies down. That's how Snickers was taught, and that's how many others were taught around here - no force, no pulling, no throwing to the ground or disbalancing by pulling legs in the air. However, if it is done not when the horse is ready or with too much energy in the cues, it can become dangerous, because I've seen horses acting up dangerously, even rearing, when it is asked incorrectly. Or just doing nothing at all, on the other hand, if the trainer isn't being clear enough. So I'm glad you're leaving this for later, when you and your horse have gained more experience. ;)
Sitting comes from lying down. I think I described the process in one of the previous comments.
You can also teach your mare to hug you. Stand right by her shoulder and, using the lead rope attached to your rope halter, ask her lightly for lateral flexion, so that she "hugs" you with her neck. Praise her, and with every next time try to keep her like this for a couple more seconds, a treat can be used at his point, and a vocal command for when you will be trying this at liberty.
I have come a long way, to surrender my shadow to the shadow of my horse.