Most drugs of abuse use the brain's natural reward system to achieve artificial highs. The natural reward system works by sending dopamine (a neurotransmitter that has happy effects) when a behavior that is necessary for survival is performed. This encourages the brain to repeat this activity.
Drugs work in one of two ways. They either force dopamine to be released, or stop inhibitory chemicals from doing their job, and dopamine is released when it shouldn't be. Drugs skip the five senses and trigger rewards in the ways stated above. The brain tries to cope by reducing dopamine receptors, but that just leads to the addict taking more of the drug to reach the same high. Drugs are more addictive the faster they reach the brain. This is why nicotine patches work. They slow the delivery of nicotine, slowly making it less addictive.