I have three cues for three different gaits: trot, pace, and rack.
Pace is her default. She will pace if I'm not asking for anything particular. She paces in the pasture at liberty; it's the gait most natural and comfortable for her. It's also the gait were her heart rate stays the lowest during exercise. I always start out at a pace and ask for transitions from a pace to a different gait. Your horse probably has a different default. It's good to establish one before you teach your horse to which gears.
From a pace, here's how I get to a trot:
Start posting. Squeeze with legs every time you go up. Half halt, to send balance the hindquarters under the horse and round the back. At that point, my horse starts trotting.
Teaching them this is... Harder. First, when does your horse trot? Up hils? Over tough terrain? I first got mine to trot over poles.
Here's how you get from a pace to a rack:
(Firstly, I don't use my rack very often in competition. It isn't very energy efficient.)
Sit deep in the saddle. Put yourself into a chair set. Using a light see-saw of the reins, ask horse to put her head down (not just her head, mind you; her whole neck goes pole level.) Squeeze legs. Lay on the gas, because racking is easier when it's fast.
Bring horse's nose in just in front of the vertical and your hands up to waist height. Add more gas. Rack like crazy.