Some chain breeding chains :P -
Say you wanted a Skitty with both Wish and Fake Tears. These moves are both egg moves. Now, no Pokemon learns both these moves and is in Skitty's egg group: so you have to chain breed. Here's what you do:
First, get a male Togetic (Male) that knows Wish (learned at level 29).
Breed it with a female Plusle (Female) and produce a male Plusle (Male) with Wish as an egg move.
Now, level up that male Plusle (Male) to level 21 to learn Fake Tears. Be sure not to delete Wish for another move along the way, or else you'll have to go back to the beginning. (Also, it is recommended you keep the move you want to pass down at the bottom of your Pokemon's move roster, because the top-most moves are the ones that are forgotten if the Pokemon learns a new move while in the Day-Care.)
Breed the male Plusle (Male) and a female Skitty(Female) to produce a Skitty with Fake Tears and Wish.
One more from Marilland-
Let's say that you wanted Charmander to learn Beat Up (Beat Up is an egg move). Now, no Pokemon both learn Beat Up and is in Charmander's egg group, so you're forced to chain breed.
This time, you just simply need a connection Pokemon that's in both egg groups (in this case, Charmander's egg group and Houndoom's egg group). You would use this when you have a Pokemon that you want to learn an egg move, but no one learns it in that Pokemon's egg group (like our bully that is a Charmander). So, you get that Pokemon in both egg groups and connect the two Pokemon. For example, here you would do this:
Breed a male Houndoom(Male) with Beat Up (learned at level 26) with a female Arbok (Female) until you get a male Ekans with Beat Up.
Breed that male Ekans (Male) with Beat Up with a female Charmander (Female).
And there you have it. A Charmander with Beat Up.
See this question for another chain. Answer credit is Blitz's.
Hope I helped,