If it's a plum pit that came from a store boughten plum then you need to be aware that most such plums are hybrids and are sterile. If it did happen to grow, the likely hood of the tree being sterile and never producing fruit is great...
However... if you want to try it, then plant the pit about 4 to six inches deep this fall after the first hard frost. The overwintering will assist in cracking open the pit. Keep in mind that if you have critters, such as squirrels, they can smell the seed a foot deep in the ground or so it seems. I'd take the trouble to cover the seed, after planting, with a small section (perhaps 1 foot square) of common screen door screen. Put a few long nails through the perimeter to hold it down. that, hopefully, will deter the squirrels...
Some people insist the seed needs to be planted pointy tip down, but I don't think it really matters...
Best of luck!