For both alcohol and cigarettes, one gets addicted because of the effects of these drugs and over time becomes dependent on the use of them. 

The nicotine found in cigarettes is extremely addictive. It's alluring to some people at first, because they may find some of the effects advantageous, like a suppressed appetite, or a slight increase in awareness. The disadvantages of course greatly outweigh the advantages. But nicotine has a trick up its sleeve. It increases the level of dopamine, a chemical produced in the brain that is in large responsible for making the connection between pleasurable activities. Over time, everything you do that is related to smoking becomes a pleasurable activity, and thus you continue the trend.

For alcohol it's mostly due to the fact that it's a depressant. Other than that social aspects also play a role, along with the release of dopamine just like with cigarettes.