So, why do people get dependent in the first place? It's because alcohol increases the release of dopamine in the brain's "reward centre" which is the same combination of brain areas that are affected by virtually all pleasurable activity. For example, socialising with friends, going on holiday, getting a big bonus at work, taking drugs and drinking alcohol.
By increasing dopamine levels in your brain, alcohol tricks you into thinking that it's actually making you feel great or maybe just better about something emotionally difficult. The effect is that you keep drinking to get more dopamine release, but at the same time you're altering other brain chemicals that are enhancing feelings of depression.
Over time, with more drinking, the dopamine effect diminishes until it's almost non-existent. But at this stage, a drinker is often "hooked" on the feeling of dopamine release in the reward centre, even though they're no longer getting it.
Once a compulsive need to go back again and again for that release is established, addiction and habitual dependency takes hold. The length of time it takes for this to happen is case-specific; some people have a genetic propensity for alcoholism and for them it will take very little time, while for others it may take several weeks or months.