Instructions
Choose a Mudkip as your starter Pokemon in the beginning of the game.
Head to the Day Care Center on Route 117 and give your Mudkip to the Day Care Man. Choose a Pokemon of the same type to go into the Day Care with Mudkip. Mudkip is a Water/Monster type so either a Water or Monster type Pokemon would breed with it to produce an egg.
Leave the Day Care Center and carry on with the game. After walking around for a bit, the daycare man will call you to tell you your Pokemon laid an egg. Use Fly to get back to the Day Care quickly.
Head back the Day Care Center to obtain the egg. Walk around with the egg in your active party for awhile. After a couple thousand steps the egg should hatch.
Keep the baby Mudkip in your party to train it or trade with a friend.