Yes colds are very contagious to other people and you can spread a cold through coughing, sneezing, kissing and just being around someone who has a cold.
When you have a cold you should always cover your mouth when you cough and cover your nose when you sneeze to prevent the spread of cold virus.
Wash your hands often as well using warm water and antibacterial soap.
Stay home from school or work until you're no longer contagious with the cold to prevent spreading the cold virus to other people.