What's the best way to cover/change wood paneling?

The most economic way would be to paint the paneling in different but blending colors.

You can use drywall patching compound in the grooves. Lightly sand to remove any gloss, prime with a stain blocking primer like Zinsser 123, then paint with your color.

just paint it. But paint will not stick, you will need to paint with "Gripper" first; can get at Home Depot or any place they sell "Glidden Paint". NO SANDING needed with Gripper unless it is fibrous (wood hairs sticking out when you gently slide your hand over it). Just wipe sand; gently sweep back & forth moving to a new adjacent area slowly working across the wood paneling. Paint with a high quality "stain kill with highly gripping properties", Check to see if more fibers lift or quickly wipe sand again anyway. Gripper is the best & least expensive on the market the only one that can be painted in 1 hour. The rest need 24 hours to lock stain kill properties. Gripper can be found at Home Depot or any place that sells Glidden Paint Then you are painting paint & not varnish. The other thing is "Pickling", no prep need except maybe a wipe sand in the direction of the woodgrain. Water down the paint, 1 part water to 2 parts paint. start at a corner & paint 1 or 2 sections staying in the lines. Then wipe off with a rag. Do small sections at a time until you get used to it & go at your own pace. It actually is quicker than meticulous painting. When done apply 1 coat of Polychrylic (can buy anywhere). It's made by Minwax. The best part, all is water clean up. I have 40+ years Comm. painting & surface coating Contractor. Have fun playing with colors.

OR sponge paint or any "Faux" technique & Polychrylic when done.

Brenda I feel your pain. I have a large paneled room in the basement probably around a 16' by 40' that I painted many years ago and I never regretted it a bit. It was not a a pretty paneling and was time for a change. I did a primer and a top coat maybe even two and what a change it made! It must have been the thing for paneling when our house was built because I had paneling in my dining room which is an "L" shape off of my kitchen. I decided not to paint but remove and was I ever in for a surprise. It was glued to the drywall and I had a disaster, It meant new drywall but that is all in the past. My projects always seem to mushroom! I call it the domino theory.

That is the purpose of paneling, thin coats of "Luan" to keep the weight & cost down. It is very porous & sucks up product like a sponge, & the first coat looks like you didn't do anything. If it is unpainted and just varnish or raw: seal it up with a coat of "Gripper" then sand (just wipe sand) then put one coat of finish paint, if it feel a little rough wipe sand again then anothercoat of finish paint. In other words seal with a coat of paint or urethane & sand between coats. If you are "pickling" (also called antiquing) & have wipe sanded & put on a coat of urethane and it still feels like it will grab the fiber of a cloth/sponge, then put a second coat of "Polyurethane" (my favorite is MinWax Polycrylic can buy anywhere & best & most durable & user friendly on the market) wipe sand when dry. "Luan" is very porous & usually requires more coats of paint than normal wood anyway, just "nature of the beast". For raw regular wood, test a piece. You may need a coat of poly first or you can just paint the raw with the watered down paint & wipe off. Depending on the look you want you can paint with fuller strength paint &/or wipe with a dry cloth or a wet/rung out cloth, or apply with a paint soaked cloth. One is called "rubbing off" the other is called "rubbing on". Even if it is painted it can be pickled, just let the paint dry a bit before wiping. The shorter amount of time the more you will wipe off, the longer the time the less you can wipe. Latex paint is fragile until it cures over weeks, so if you wait too many minutes long, just keep gently wiping with a rinsed out very moist cloth until you blend in the intensity of the design. Don't try to make it uniform. All "Faux" is creating a stressed look or weathered look like an old wind blown or just aged look. So don't fuss with it, let it be what "it" wants to be. A paint job needs to be fussy & uniform coated. With Faux, just go through the motions, que sera, sera, whatever will be will be. If pickling always put a coat of polyurethane for a final coat, that will make the wood grain pop. Even in Tole Painting or decorative painting on raw wood, we always prep by: light sand, apply one coat of Poly & light sand when dry, before starting our painting project. The poly drys so quickly it is just a 30-45 minute prep, that makes a world of difference. I hope these tips help in this project & future projects that may have a different starting surface types. Hey, it's only paint & can be painted over & polyurethane loves to be painted, very compatible with most surface coatings.

Take it out and if there isn't drywall behind it, put in insulation and drywall it. You won't regret it. No matter what you do, filling grooves which is very time consuming or prime and paint it, it will still look like paneling.