Hello Camille, improve your horse's gaits is very important :) as a horse owner your goal will be to "get the gait" consistently, without your horse reverting to a trot or pace. Further, you need to make sure he isn't performing a stepping pace, which is smooth to you, but will wreak physical havoc on him over time.
Before you begin, make sure your horse is comfortable in his tack, and has plenty of freedom through his back. Discomfort or physical restriction of any kind will sabotage your best efforts.
Plan to ride with the impulsion aids with which you're comfortable, such as a crop, spurs, or long reins. To perform a correctly timed saddle gait, your horse has to use every muscle in his body. Therefore, you must insist on this gait as strongly and persistently as is necessary.
In first, ask for an active walk. Mount up, and ask your horse for an active, vigorous walk, but don't allow him to jump up to a faster gait. If he does, apply a light rein cue to check him, while simultaneously using your seat and leg to keep the forward momentum. Ask him to walk as fast as he can without changing gait. I call this exercise "working the walk."