You can help ease a cough and help it go away within 24 hours or a few days by taking some cough medicine a few times per day.
You can also take a steamy shower and use a humidifier in your room to help get the moisture in the air as moisture in the air helps you breathe better and helps get your lungs moist which can help ease a cough.
Staying hydrated with plenty of water or warm tea with some honey can help alleviate a cough that won't go away and keeping yourself hydrated can slow down the coughing and can help prevent the coughing from happening as much.
If you smoke you should stop smoking as well and avoid being around smokers because smoking or being around second hand smoke can cause your cough to get worse and cause other health issues.