Why would a new CD skip on a new player?

If it's a portable, it may need new batteries, unless it has a battery meter which is showing more than one bar- a lot of portable CD players (especially boomboxes) don't have a battery meter, in which case the only way you know is if it randomly skips, randomly shuts off in the middle of the song, or it plays slowly (I honestly don't know what those kinds of players do on low power because mine has a battery meter.)

If you bought the PLAYER at the store and you bought a supposedly working display model (it was the last one and the store was willing to sell it) it may just be a dirty lens. Top loading models are the easiest to clean, because you can just open the lid and wipe the lens with a Q-tip dipped in alcohol (the Q-tip, that is, not the player :)
For drawer or slot loading players/drawer loading "changers" a cleaning disk should suffice, but look in the manual of the player to see if there's any warnings about cleaning disks. If it says not to use them for whatever reason, use a compressed air can and "spray" it into the open drawer/slot

If all else fails, try a different CD in the player. If that CD plays, then it's your other disk. If that one doesn't work, you should return the player and ask for a new player.

could be a flaw in either the player or the cd. I would try an old cd and see if it skips too then I would place the new cd in an old player. should be able to tell if one or both bad.

When that happens, I just wipe it down with a static free cloth and it usually plays ok after that.

Defective-When it was pressed it was either warped or the top coating was inconsistent. Not that uncommon. Sometimes washing them in dish soap fixes the problem-otherwise return for a new one.