Don't you just tap their legs a bit until they hop around? Then pull their heads in a little while tapping and eventually they'll lift their legs up?
OR try riding over some hot coals, sure fire way to get elevation
Sorry mate I don't mean to stir, maybe go for a wander over to the english and dressage subsection and check out some of the posts about on the bit, collection, engagement etc.
Dressage is not easy - though it looks like the rider is doing nothing, and people who do not do dressage like to say that it is nothing more than riding in circles and doing 'boring' float work, this is a long way from reality.
Dressage takes a lot of conditioning, gradual training, knowledge, skill, feel, timing, balance and patience. You start at the basics - an ottb will need to establish basic 'stop go and turn' before anything else. Gradually increasing this to working with increased engagement, then starting to swing the back, understand a contact and so on until happily working into the bridle over the back aka 'through' or 'connected'.
From here, we start to ask the horse to gradually shift more weight onto its hindquarters, ask for more connection and suppleness through the entire body. Gradually, we will demand more 'sit' and increased balance/self carriage, until the steps begin to develop more elevation while maintaining forward thinking.
It's all about steps, you don't move onto the next step, until you've finished the one before. Think about building a horse. You wouldn't start to frame until you'd laid the foundation. Same goes for training a horse. You don't get that light, elevated trot until you have basic aids, suppleness and sensitivity, along with strength.
Find yourself a qualified and proven dressage trainer, and go from there. If you try to do it on your own from square one, and have the mindset of wanting to do 'flashy' movements like they do in grand prix, all you'll do is burn out your horse's brain and body, sending it into a downward spiral of confusion and frustration.