Ohhh!! this is so much fun!!
I run a local rescue and all our too-small-to-ride ponies are taught unmounted agility :) The kids who volunteer each teach their own pony how to do all the obstacles.
That being said - There are several ways to teach a pony to do agility, the traditional horse training way (Pressure and Release) where you lead the pony around and over the obstacles. You could ground drive the pony - I wouldn't risk it, there's too many lines to get tangled in and not enough feel to release and not pop them when they jump. But to be honest - both of these ways are pretty boring and you end up jumping more than your pony!
The way we train the ponies is through Positive Reinforcement training. It's a training style you've probably seen alot for dogs. The methods were scientifically researched and developed by sea world for training marine mammals (as pressure+release and punishment don't work for them!). It's also called "clicker training". You use a clicker or some other audible bridge signal to bridge the moment the horse makes the right choice with the food reward they get later.
I use this method because it allows me to train the horses at liberty, it's enjoyable for both of us equally, I can mold each skill to be more the way I want to see it. For example, my pony is a bit too big for the jumps we built for our minis, so often he'd trot over them, rather than jump them - so soon I started only bridging and rewarding when he actually jumped. Then I started fine tuning that for when he jumped well, tucking his legs more nicely and actually working for it.
I usually start the ponies by teaching them to stand still and face forward, next to me, calmly, with all 4 feet on the ground. I do this by standing at their shoulder with my pouch full of treats and waiting. When they stop moving, mugging and moosing and face forward (even for just a moment) I bridge+feed. I repeat this until they no longer do anything besides stand still and face forward. This helps make sure they'll always be polite around the food and never try to mug people. It also provides them a skill to go to when they aren't sure what they're supposed to do. I do this for about 5 minutes at a time, about 5-10 times (depending how rude they are to start - some well mannered horses only need a couple) I go until I can walk into the arena with the horse at liberty and the horse comes and stands beside me without ever invading my space or sniffing for food.
Then I teach them to target - this is so fast and fun for the horse! They find "the food button". I do this by holding out a target (most of the kids have either made their own with some decoration on the end of a stick or bought those colorful riding bats - I use a crop with duct tape on the end to make it more visible) in front of the horse's nose, most will sniff it out of curiosity, at this point they know the bridge signal from your initial training, so when their nose touches the target you bridge+treat. Repeat this until you can move the target all around and they always touch it. Then you can use this to teach them to lead, following the target, at the walk, trot and canter.
Then you just add obstacles!
With Clicker Training you can refine skills to build better jumps and weaves and help them overcome fears of specific types of jumps or obstacles.
My pony (Punk) came to our rescue because he was extremely aggressive, after trampling his professional trainer who was trying to ground drive him. So he came with a bad Rep! So I got to work with him, instead of the kid volunteers. Punk'n when he first started learning about jumps:
This is one of our volunteers with a pony rescue who was completely feral on arrival, spent the first 12 years of her life loose in a herd on a small reserve, never handled. Now she's doing unmounted agility with this little girl :)
Here are some pictures of our obstacles, we had a little pony parade fund raiser a while back where the kids each showed their pony's agility
This is another obstacle we've been using lately, getting them used to tarps on the ground and even hanging them up over jumps to be like walls that rattle - trying to make things scary cause these ponies are getting too good! I don't have a pic of this with the unmounted agility, only ridden work:
I hope this helps, if you're curious about learning more about Clicker Training and how to do it with your ponies here's some good links:
This thread has some valuable info on the science behind CT, why it works so well for all animals (not just dogs) as well as some good "how-tos" Clicker Training: Challenge Accepted
This is my favorite professional horse Clicker Trainer, her website is full of free
training videos and guides, as well as blogs full of "how to" and trouble shooting :) Shawna Karrasch and On Target Training | Positive Reinforcement Clicker Training | Horse Training
I hope you have tons of fun with your minis!!