Oak, like most woods used in furniture making, is fairly easy to clean. Start by dusting your oak furniture piece with a soft cloth. If there is a lot of dust, use a damp soft cloth to prevent the dust from billowing out and resettling onto the furniture piece. Do not use feather dusters or similar devices, as these will spread the dust into the air and right back onto the furniture.
Dilute a soap-type furniture cleaner according to the manufacturer's recommendation. A good oil soap will help highlight the beauty of the grain of oak furniture. Murphy's Oil Soap is the most well-known brand, but others are available. Dampen another soft cloth and wring well. Rub the furniture with the grain of the oak and remove and excess solution with a dry cloth or paper towel.
For areas that cannot be reached with a cloth, use a soft-bristle toothbrush. Dip the toothbrush into the solution and tap off the excess. Then lightly scrub the grooves, corners and other hard-to-reach areas. Use a paper towel or dry cloth to soak up any excess solution.
If you have an old piece of oak furniture that has a lot of wax build-up, you will need to strip it down to the original finish first. Furniture wax strippers are available in the cleaning supply section of many home improvement stores. Read and follow the manufacturer's directions carefully. Test the solution on an inconspicuous spot before applying to the entire piece. Apply with a soft lint-free cloth or, for difficult spots, grade-0000 steel wool. Rub with the grain of the oak and repeat as necessary until all of the wax build-up has been removed.
Do not use wax-based spray-on cleaners, as these will dull the contrast in the grain of your oak furniture over time.
Do not try to clean unfinished oak with this method. The solution could stain the wood.
Read the manufacturer's directions on the soap or wax stripper, especially dealing with safe use, and adhere to them.