Playing at Liberty with a horse is with no halter or lead on the horse. You'll want to start in a round pen but you certainly don't chase the horse around lol. You want to PLAY with her. See if she will follow you around, trot when you trot, stop when you stop, back up and come to you. It's very low key and it's fun! But, you want to have a good foundation on a line before you jump into liberty work. So on the lunge line so things don't get boring, try using obstacles like I said in my last post. Sorry, I wasn't clear about what to do at Liberty and what to do on a lunge line
You'll want to do the ground poles, going over tarps, etc. ON LINE.
One thing you can start to teach her is a game I LOVE to play with my horse called "stick to me." You'll start on line to teach. Basically you want her to mirror your every movement. Stand at her shoulder, bring your energy up and make it obvious in your body and walk forward. If she doesn't follow, reach back and lightly tap her with your whip to say "Hey, follow me." For this game, it's best if her head is a little in front of you or you are at her shoulder, but don't let her get too far out in front of you otherwise you will lose control. When you stop, exhale big and bring your energy down. If she doesn't stop wave your whip in front of her to tell her that "door" is closed. Then stop and rub her. Once that is good, then start this at the trot. Get your walk, trot and stop good. Now is when the fun begins!! You can trot, stop, back up, trot off immediately, stop, spin around, turn, etc. and she will be right beside you. But it all builds on itself, so take your time. Oh, and when you ask her to back, tap the ground with your whip in front of her as you are backing, and if she doesn't respond put a feel on the halter to ask her to back. When she does, release and praise. Then at some point you can even do this at the canter! Remember to use your whip like a mare's tail. If she doens't follow or turn with you, lightly reach back and tap her or swing the "string" end of it at her butt, but be careful that it doesn't snap her with you swing it!
This is such a fun thing to do with your horse! Once it's good on line you can then do it at Liberty. My horse really gets into it, I'll trot off, stop, back, trot off again, then canter, stop, back up, spin around and go the other way, and he's right there having a blast! Let me know if you are unclear about something.