Regarding the verbs for different types of sports, which one should I use for which sport?

This is a common question, as in English we generally same someone plays a sport, but the verbs vary in Mandarin. An easy way to remember the correct verb for the corresponding sport is to think about the exact action you do when you are playing the sport. 

E.g. 1, you kick a football. Therefore, you 踢 (kick) 足球 (football). 
E.g. 2, you hit a tennis ball. Therefore, you 打(hit) 网球 (tennis ball).