Smoking an e-cigarette is essentially the same as smoking a regular cigarette. As you draw on the e-cigarette, an airflow sensor within the battery triggers the battery to activate. This activation creates vapour from the cartomiser and the LED on the end of the e-cigarette glows.
You draw this vapour (which contains nicotine) the same way that you would a regular cigarette. The flavour can vary, with a number of traditional flavours (Tobacco and Menthol variants) as well as fruit (Apple, Vanilla etc) and 'exotic' flavours such as Energy Cow (We can't use the trademarked name, but there is an energy drink named for the male cow....)