Building muscle strength comes down to two things: exercise and nutrition.
Consider experimenting with eccentric resistance training – slowing down the eccentric phase of muscle contraction. This method will cause the muscle to sustain greater levels of cellular damage and result in further cellular repair, which in turn means increased strength and muscle mass.
Protein is essential for gaining strength, as it is what the body uses to build the muscles back up to react to increased demand. Insufficient protein intake can hinder your efforts in the gym. Some people find it hard to eat sufficient protein throughout the day, in which case protein shakes may come in handy; however, real food is usually a better source for protein than supplements. Most people only need about 0.8-1g of protein per pound of lean body weight (not total weight) per day.
When it comes to building muscle, the best approach will depend on each individual person. Talk to your trainer about what you can do to build your muscle strength.