Whenever I have a dry cough I up my fluid intake to keep my body more hydrated and take steamy hot showers.
The water and other drinks keep my mouth and throat moist and the steamy hot showers also add moisture to my lungs which help get rid of a dry cough.
Drinking hot drinks such as hot tea can also help get rid of a dry cough as well as taking some lozenges and using an air purifier to get rid of irritants in the air that could be causing your dry cough to worsen.
Adding some honey to some warm tea can also help get rid of a dry cough as well as sucking on peppermint.