Congratulations on your new horse!
Is your horse a TWH? This is the breed that I ride and train, and show here in Alberta.
You may not be cantering yet, and if you do have a TWH, there are differing opinions on cantering. Since someone on this thread has told you NOT to canter your horse, I would like to offer a differing view point.
When you are ready to canter, go for it. I show 3-gait with my walker, and they have the most beautiful, slow canter. Many trainers in the states do not canter their walkers because they want them to run walk as fast as possible.
I do agree that you should have a nice flat walk and run walk before moving into a canter, just as you would walk/trot a trotter before cantering.
Getting your horse to gait, you could definitely use a good trainer on the ground to help you get a feel for when your horse is "hitting" it so to speak. If possible, ride another gaited horse who does gait so you can really get the feel for the rythym.