Suppose there is a person that has never used nicotine in any form in his/her life. Why does the person get dizzy after a few "shots" from a cigar(nicotine)? What's the difference between using other plants(e.g. marijuana)?
It's all about the synapses, the places where separate neurons connect to one another. All psychoactive drugs act in some way so as to modulate the signals that are passed from one neuron to another. Nicotine acts by increasing the effect of signals that pass through a particular type of synaptic receptor called nicotinic acetylcholine receptors (they're named after the fact that they're affected by nicotine). The dizziness and other effects of nicotine are caused by this interference with normal neuronal communications.
The reason why regular users of nicotine don't get dizzy is because they've gained a tolerance to the drug. Tolerance isn't super well understood at the molecular level, but it has been associated with long term changes in the quantities and types of receptors that are present at synapses in certain regions of the brain, it particular the nucleus accumbens.
Marijuana is similar to tobacco, only its main psychoactive component, THC, acts on the cannabinoid receptors.