It's awkward the first time you do it, but it's really awesome. irc://irc.furrychapel.org/#uno is the location. http://foxnet.in/fun.html#Uno is the manual. Type !uno to start a game, and jo to join the game; if no other people join, you'll play against the AI!
I've earned 6,302 "Skittles" so far playing the game; it helps that winning streaks and setting certain records gets you extra Skittles, and I set those records early on due to the bot being fresh.
Edit: The code of the Eggdrop bot is at http://pastebin.com/PkETdMdT . Flechmen says if I can find and/or program more games that I'd like GameBot to be able to play, and they're in Eggdrop format, he'll add them.