Make a Solution
Mix 4 cups of water with 4 cups of distilled white vinegar along with 1/2 cup of baking soda to form a solution. You can use any brand of vinegar or baking soda as they are easily available from any nearby store. Be sure to carefully mix the solution as you do not want it to be too strong. Try to maintain the perfect balance between baking soda, water and vinegar for best results.
Scrub and Wipe
Using a kitchen sponge, dip into the solution and wipe the cabinets vigorously. Work with the grain of the wood, re-apply and wipe as needed. Continue to do this until the cabinets are cleaned. Take your time as you use the sponge to wipe the cabinets. You will want to cover the entire surface area of the cabinets. Also, do not forget to get some solution inside the hard to reach corners. Remember to just dip the sponge in the solution as you do not want to soak it but just keep it a little damp.
Wipe With a Wet Cloth
Dip a clean cloth in warm water and wipe all of your cabinets to remove whatever solution and grease may be left. Thoroughly wipe all the surface areas of your cabinets with the clean cloth. Carefully remove all of the solution and grime that might still be on the cabinets.
Polish and Enjoy
Use an after-market polish that you can purchase at your local grocery or hardware store and use it to polish your cabinets. Follow the product's instructions. Doing this will protect your cabinets from future grease build up and have them looking their best. Take your time as you apply and wipe the polish from the cabinets. You will want to make sure that you cover the entire area of the cabinets for a nice finished look.