Two important characters to do with ball sports are 打 (dǎ) 'to hit' and 球 (qiú) 'ball'. 打 can be used with most ball games to mean 'to play'. By adding a specifier to 球 you can indicate what ball game is being talked about.
Examples
打网求 | (dǎ wǎngqiú) | 'to play tennis' (literally, 'hit net ball') |
打足球 | (dǎ zúqiú) | 'to play football' |
打高尔夫球 | (dǎ gāo'ěrfūqiú) | 'to play golf' |
打篮球 | (dǎ lánqiú) | 'to play basketball' |
To say where the ball game takes place you can use 球场 (qiú chǎng) 'playing field'.