The following videos show you how to make a home-made lava lamp. It is very simple - grab a clear cup (or bottle or vase or flask), fill it about a third full of water and two thirds full of oil. The oil floats on the water as it has a lower density. Add some food colouring (you can do this at the start directly to the water, or after you have added the oil - this has the added benefit of showing that the food colouring does not dissolve in the oil, so it drops through the lower density oil to the water below).
You may already have Alka Seltzer in your medicine cabinet - it is an over-the-counter pain reliever containing Citric acid and Sodium bicarbonate (also known as baking soda). Split the alka seltzer tablets into about 4 bits, and add them to make your lamp. See the videos below for what happens.
The reaction that is occurring is:
Citric Acid + Sodium bicarbonate → Sodium citrate + Carbon dioxide + Water
C6H8O7 + 3NaHCO3 → Na3C6H5O7 + 3CO2 + 3H2O
Or more simply:
3H++ 3HCO3- → 3CO2 + 3H2O
Note, if you don't have alka seltzer, you can try baking soda, but add some vinegar to the original water mix, as vinegar is acidic and provides the H+.
When you add the alka seltzer to the water, the citric acid and sodium bicarbonate start to dissolve, which allows the reaction to start and is why they don't react in solid form in the tablet.
The reaction produces gaseous carbon dioxide, which has a lower density than both water and oil, and hence rises through the layers. When the gas bubbles exit the water into the oil, they trap and pull up a small amount of water with them. When the bubbles reach the surface, they burst and the water falls back through the oil. It's worth looking at this closely, as you will observe coloured water droplets that don't have quite enough CO2 stuck to, or dissolved within, them to make it all the way to the surface, and so they float around, buffeted from side to side by other, more vigorously moving, droplets.
Here's some more over at CSIRO.