First, familiarize yourself with the Dressage Training Pyrimid and the Test Objectives. These are good roadmaps for training - since the tests are designed to build the skills in a logical and practical progression.
For example, at Training Level, the purpose is to "confirm that the horse's muscles are supple and loose and that it moves freely forward in a clear and steady rhythym, accepting contact with the bit".
Translation LOL, is that the horse should be generally balanced, maintain a consistant, forward (working) tempo in all gaits and the horse should be acceptiong contact; the horse should be on the bit or slightly in front of the vertical. The horse should understand how to bend, respond to half halts and be well balanced through the transitions.
Next, a good understanding of the court geometry is helpful. The geometry used in the tests is not random; again it is designed to promote a progressive system of training.
Lessons are highly beneficial, but if finances or time prohibit this, there are other ways to collect knowledge:
Go watch some shows; better yet volunteer to scribe. There is a wealth of knowledge to be had (and its FREE!) If there are barns in your area that allow you to audit, go and watch various lessons, observation of riders of your level and above will give you lots of insight that can be applied to your own workouts with your horse.
Warm up properly: a stiff horse cannot perform at his highest level - make sure to really loosen up his muscles with a good warm-up (and don't forget the cool down when you are done!)
Read: Although books cannot teach you to ride, they can help you understand concepts better. Sometimes our instructor will tell us something 50 times, yet it takes someone else explaining it with different words to really make it "click". If you are a fairly educated rider, you can take the information you read and apply it to your self-schooling sessions.
Test yourself: even if you don't plan to show, ride through the tests periodically as a measuring tool. Where are the weak points? The strengths? What has improved since the last time you tested yourself? Has anything gotten worse? (Don't laugh, this happens! ;) )
Oh..and don't forget to practice the walk, free walk and halt! These are just as important as any other movements and are often overlooked or under-appreciated. Remember, the freewalks have a co-efficient of 2 in many of the tests - don't waste points because you didn't give it the respect it deserves....I've seen many otherwise well-schooled horses blow it on the free walk.
Finally, have fun! Dressage is hard work but its also highly rewarding. Make sure you don't over drill yourself or your horse. Make sure you make time for a bit of relaxing and play too...