2. Never Train Just in Straight Lines
Many situations occur during the course of a match that require a multitude of movement types, but very few situations call upon you to run forwards as though you were sprinting to catch a bus.
So why would you choose to do your speed training in this way?
As I mentioned, if you were training for the 100 meter, then straight line running is acceptable. But for tennis--and most other sports--you have to learn how to move quickly in many directions.
Straight-line training has its place in your program, but should not be the only type of speed training you do.
3. Only Train Over Short Distances
Another aspect of your speed training involves the distances you should be doing your training over.
When you are training for speed, you only need to be training over very short distances such as 5 – 10 meters/yards.
To re-visit our earlier analogy: You are not a track sprinter so don't train like one!
4. Don't Forget your footwork
It's OK training yourself to move faster, but at some point you have to get to the ball and be able to adjust your position to be able to hit the ball well.
Too close or too far away and you won't be able to make a meaningful shot.
Also, more often than not, you will have to hit several balls in a row which means recovering well after one shot and getting to the next ball, which requires good footwork.
You cannot have good on-court speed without good on-court footwork!
So get yourself doing ladder drills, cone based agility drills, etc.
Anything to challenge your ability to stay balanced while moving around quickly.