What is the best way to cover up paneling?

Diluted ammonia is good on walls. And especially for kitchen grease. Get a bucket or spray bottle and wipe down paneling with warm water and ammonia. Gloves are needed.

Then paint.

The best way to cover paneling is to paint it! We did a whole house this way. First we were told to caulk all the cracks between each panel. Then we painted with aroma free Kilz primer paint. Then we painted each room any color we wanted. The Kilz really covered the paneling. In the front room the cheap paneling was wavy so cover that up I sponge painted 3 shades of the green we chose. We painted solid with the lightest green, then used a sponge or plastic bag to sponge paint with a slightly darker hue of the same green, then barely added the darkest hue of green as the third touch. It was beuatiful. We added a wallpaper border at the top of the room for a finish. I made the drapes and we purchased sheers for the windows. The room looked light, cheerful, and bigger. It was the wisest choice we made for that house and we doubled our money on it when we sold it 3 yrs later.

Hello, Robin! Here is what HGTV recommends when painting paneling. Click on the link below to view their guide on how to go about it. Good luck!

http://www.hgtv.com/design/decorating/design-101/painting-wood-paneling

https://www.thespruce.com/paint-wood-paneling-2213358

Here are some more options!

http://www.housebeautiful.com/design-inspiration/home-makeovers/g2624/wood-paneling-makeovers/

https://www.pinterest.com/explore/wood-paneling-update/

http://homeguides.sfgate.com/make-wall-wood-paneling-look-modern-60464.html

http://homeguides.sfgate.com/update-old-paneled-walls-33819.html