To achieve power athletes need to train their body from the inside outwards, Abdominals first, back muscles next then arms then legs. See the section on Core Strength and Isometrics
Nutrition is also very important and Protein provides the building blocks of muscle. Many athletes waste time on training because thier nutrition is inadequate to build the required muscle prior or post the training session. (See the section on nutrition)
Muscles only contract and relax - they do not have a pushing effect. Muscles are generally in groups that work opposite to each other. Biceps v Triceps is a typical example of the upper arm.
To build bigger muscles you should do low Reps 3 - 5 but heavy resistance so that the maximum you can complete is 3 to 5 Reps. Rest and then do 2 more Sets (a Set is a repetition of the reps). So you complete 3 Sets in total. Always do a half weight/resistance set to warm up. To be strong but trim and lean you should do high Rep but low resistance training (light weights or resistance).
50 to 100 reps. However, you should build up to these figures slowly. Starting with 5 or 10's rest and then two more sets. Gradually increasing the numbers over time as you become fitter and stronger.
Athletes can often be extremly strong on say a bench press or lifting weights, but have trouble applying the power in different sporting situations or unusual conditions. This is because of the way they train.
To achieve overall strength and power all the muscles need to be close-linked. In other words your body is like a chain it is only as strong as its weakest link. Special linking exorcises need to be done to achieve overall strength.
A strong abdomen will be of little use without an equally strong back. Legs and arms are only half power without good core strength etc etc.