Many trainers don't know what they are doing and like to chit chat more than anything, true. For some people, they want a therapst and motivator to do a little exercising. There are other trainers that are more knowledgeable and can be of great help in showing proper technique and developing a program. Your body is not a simple piece of machinery like all the others that will respond in the same way.
Anyhow, three months is short. The notion that working in a specific area will cause you to burn fat off in that area is nothing but a wives tale. More muscle mass will increase the rate at which you burn calories and convert fat, but not in a localized area. As was mentioned above, diet is just as important.
The swiss ball is king for abdominal a and back exercises. Of course, if you only focus on specific body parts and neglect others, you can cause imbalance that may result in injury on or off the court. Chek out coreperformance if you are really interested in strengthening your core while addressing overall fitness. For more volley specific performance, if you only did squats and deadlifts PROPERLY your glutes, legs and core would receive extreme benefits while supporting your on court performance.
I would caution on JP Mac's advice. While he mentions a number of great exercises for the lower body, unless you are performing them properly and have developed an adequate strength base (primarily aongst your tendons and ligaments) you can run the risk of injury.
You don't really need any fancy exercises or equipment to make fitness or athletic gains but you do need to be smart about what, how and when you work out.
Here is a site with some exercise animations:
http://www.exrx.net/Lists/PowerExercises.html
It is still helpful to have someone watching your technique, because you can't always judge for yourself.