Determine whether the lamp was turned on when it broke. If the lamp was running, the wax it contains will most likely be predominantly liquid. If the lamp was off, the wax will be in a more solid state.
Remove the broken glass first, wearing rubber gloves. Pick up the large pieces of broken glass and dispose of them in the trash.
Pick up any chunks of solidified wax, while wearing the rubber gloves, if the lamp was not running when it broke. Toss the wax into the trash.
Wipe up the spilled liquid from the lava lamp, using disposable paper towels. Continue to wear the rubber gloves, to protect your hands from any small pieces of glass remaining in the spill area. If the lamp was running when it broke, there will be a larger volume of liquid, because some of the wax will have melted from the heat of the light bulb. Dispose of the soiled paper towels in the trash.
Soften any wax that has hardened onto the wood floor using a hairdryer. Set the dryer at a medium heat level and direct the air over the hardened wax. As the wax softens, scrape it off with a plastic scraper, then wipe the area with a soft cloth or paper towel.
Clean your wood floors with your usual detergent or with a mild solution of water and vinegar. A mixture of 1/4 to 1/2 cup of vinegar in 1 gallon of warm water is ideal. Allow the floor to dry naturally after washing it.