How does a volcano for a science fair work?
The food color-dyed water is just there to add volume and color.  

The household chemicals used are acetic acid (vinegar, $\ce{CH3COOH}$) and sodium bicarbonate (baking soda, $\ce{NaHCO3}$).  

The acetic acid and sodium bicarbonate react to form carbon dioxide gas ($\ce{CO2}$), dissolved sodium acetate ($\ce{CH3COONa}$) and water ($\ce{H2O}$).  It is the liberation of $\ce{CO2}$ gas that causes the foaming and bubbling.

The chemical reaction is written as:  

$$\ce{CH3COOH(l) + NaHCO3(s) -&gt; CH3COO-(aq) + Na+(aq) + CO2(g) + H2O(l)}$$  

Where:
l = liquid
s = solid
aq = aqueous (dissolved)
g = gas (vapor)