The most common way to say "playing badminton" in English is simply "playing badminton." This phrase can be used in a variety of contexts, such as asking someone if they want to play or talking about your own experience playing the game. Another way to say it is "playing shuttlecock," which emphasizes the object being hit back and forth.
When it comes to actually playing badminton, there are a few key tips to keep in mind. First, make sure you have the right gear. This means having a good quality racket, comfortable shoes with good grip, and appropriate clothing for the weather and level of activity. It's also a good idea to have a few shuttlecocks on hand in case one gets lost or damaged.

Next, make sure you know the basic rules of the game. Badminton can be played in singles or doubles, and the rules vary slightly between the two. In general, the goal is to hit the shuttlecock over the net and land it on the other side without the other player(s) being able to return it. If the shuttlecock hits the net or lands out of bounds, a point is awarded to the other side.
Finally, practice and communicate with your playing partner(s). Badminton is a game that requires good coordination and communication to play well. Make sure you are hitting the shuttlecock to each other in a way that allows the other person to return it, and work on developing strategies for setting up and executing successful shots.
In conclusion, playing badminton is a fun and popular way to stay active and socialize with friends. Knowing how to say "playing badminton" in English and following some key tips for playing the game can help you have a great experience on the court. So get out there, grab your racket, and start playing shuttlecock!