Cut the fish into ½-inch pieces or slightly smaller.
To marinate the fish, place in a glass or plastic bowl and mix in the onion, black pepper and lime juice. Cover and refrigerate, stirring frequently, for 45 minutes.
When ready to serve, add about a teaspoon of salt to the ceviche and mix well (the saltiness of the juice will dissipate as the fish absorbs the flavors.)
Scoop the ceviche onto a smallish, deep platter, then dot with avocado and cilantro leaves. Serve as an appetizer to eat with a fork, or use tortilla chips for scooping.
Notes
Look around for some good quality fish for this recipe. You really need a nice looking piece of firm, white fish that is sashimi-grade quality. Don't go cheap on ceviche.
It's ok to make this a few hours (2 to 3) ahead of serving time, but keep well-chilled.