Remove the cigarette from your mouth. As you take it out, inhale the smoke into your lungs by taking a deep breath. This will help avoid irritating your throat and triggering the cough reflex.
Note that this is not like smoking a joint, where you inhale directly into your lungs.
An alternate form of inhalation is called "Frenching". To do this, before you inhale, push some of the smoke back into the air (without exhaling), and as it exits your mouth, suck it in with your nose. This may take some practice to perfect.
As you continue to smoke, your tolerance for the smoke will increase. This is where the problems arise: the more tolerance you have for the sheer act of inhaling smoke, the easier it will be to smoke. The more you smoke, the more nicotine you ingest, the more addicted you get as you build a tolerance for nicotine. To get the same feeling you did from your first cigarette, you need greater amounts of nicotine, which makes you smoke more.