A lot of oil painters use disposable paper palettes or plastic ones with a few using glass. I do not like any of these. The paper palettes absorb oil and plastic and glass are too slick and plastic is reactive to even mild chemicals. A traditional palette of wood is best. While some traditionalists insist on using a palette of pear wood a cheap plywood palette which can be had for less than eight dollars at an art store will work great if pre-seasoned correctly. I will teach you how to do this.
While plywood is somewhat rough naturally when you get a new palette inspect it for especial roughness. If it is rough you will want to sand it. Check especially around the edges and the thumb hole. Remove all sharp edges. Comfort is key. Use a fine sandpaper and glide the sandpaper over the surface until it is no longer rough, but remember that it should not be especially smooth and certainly not mirror-like at this stage, just without sharp edges, splinters, or bad chips, all of which would tear up or your brushes. Because the sand left behind by the sand paper will also tear up your brushes you must make certain that it is entirely removed before going on to the next step so take a cheap nylon brush (like those used to paint houses) and while holding the palette at an angle that would allow the sand dust to fall beat the surface of the palette all over time and again until you are certain that all of the sand has been removed.
Now you will need linseed oil. Saturate the palette on both sides with linseed oil allowing the wood to absorb as much as it can and leave it for a day or so. Wipe off the excess oil and using a scoop made of paper (do not use a plastic spoon because the static will repel the pigment making a mess) sprinkle a dry earth-tone pigment (I like to use English red because it is pretty) to the surface and rub it in staining the wood and polishing the surface and filling the grain. A lot of rubbing here is desirable as is a lot of pigment, but only use enough pigment to allow for easy rubbing. Placing the palette on a table (with lots of paper underneath to protect your table) use pressure to polish, but be careful not to crack the palette. Polish the surface as much as you can within fifteen minutes or so and wipe off the excess. You should do this on both sides even though you only need to focus on the side you will use. Remember that you are staining and polishing the wood, not painting it so do not use more pigment than necessary and certainly do not leave excess just wipe off the excess and hang on a nail somewhat away from a wall to dry for three days. If you do not have dry pigment you can put some oil paint on newspaper moving it around occasionally to let the newspaper absorb almost all of the oil and use that.
Repeat the staining and polishing process over the period of maybe two or three weeks until the wood is well sealed, seasoned, stained, and polished. You do not want to create a mirror like finish, just a well used look. Each layer will require less oil. Do not use any drying chemical during the process, just let it happen. The last layer (three or four layers may be enough, but ten is not too many) should be very dry and hard before you try to use your palette since any chemical you try to add to your oil paint such as odorless mineral spirits may attack your finish if it is not entirely dry when first used.
Now in order to make use of your palette you will need to learn to clean it correctly. If done properly the palette will only increase in beauty and natural tack so that it will hold paint better and better and be continually easier to clean.
The first rule is to clean your palette immediately after use. Never let paint dry on your palette. The second rule is to never use chemicals or soap to clean your palette. Instead simply take a paper towel and wipe off the large globs first and then using the clean portion of the paper towel clean the rest with a rubbing action polishing the entire surface turning and folding the paper towel as needed until the paper towel comes away from the palette clean. To create an even polish use the portions of the paper towel which have paint on them to polish areas that had less paint. Make sure the surface is clean before putting your palette away. This process will season your palette year after year making the palette better with time.
Even a pre-seasoned palette will at first require considerable pressure to properly clean as your palette ages the surface will become more well polished and will be much easier to clean. If a little paint remains in the grain of a young palette it will not hurt it as it must be filled eventually, but try to get it clean.
While you should never allow paint to dry on your palette if a bit of paint dries on the surface you can use some of the other paint to polish it off. It will take some rubbing, but it will work. If a large glob of dried paint will not come off you must allow the palette to dry completely so that you do not embed sand into the finish and afterward you may use a very fine sandpaper to remove the glob and then you may remove the sand with the brush as before and re-stain, re-polish, and refinish that spot. Eventually the spot will blend in with the rest of the surface fairly well.
A lot of artists do not understand why they should go through all of this trouble to season a wooden palette. Those artists have never painted on a well seasoned palette. The natural tack of a wood finished with linseed oil is perfect for holding oil paint and a well polished surface is incredibly easy to clean. The object is also very beautiful looking more well polished and colored than the finest of antique furniture and such a personal object stands as a testimony of the years dedicated to your craft and that help to remind you of who you are and what you do helping to establish a powerful individualistic identity which is lost through the dispose-ability and plasticity of modern tools.