Can you suggest tips/exercises for skinny guys on losing body fat and gaining lean muscle?

Increase in cardio. If you have adipose tissue that you'd like to lose then consider an increase in cardio and a balanced diet. However, do not always do the same exercise or you will increase your risks for stress injuries. Mix things up with running, biking, swimming, or circuit training. Core exercises may build muscle, but to burn fat you need to burn more than you consume and cardio is key!