Counter and Me First are both Egg Moves for Rattata, so you'll have to breed
To get Counter, you'll have to breed a Rattata with a Slackoth, Vigoroth, Slacking, or Lucario that knows Counter.
To get Me First, you'll have to breed a Rattata with a Sentret, Furret, Stantler, Absol, or Lucario that knows Me First.
I'm not sure if there are any special things that you have to do to breed for Egg Moves,so if there is anything extremely important that I missed, please tell me!
Hope this helps!