thinly sliced fennel forms the base. you can use a mandoline to make sure it's extra thin, but i recently cut myself badly on one of those monsters, so i used a knife for this.
wash the fennel bulb (also called anise) and trim the bottom off. cut in half down the middle of the bulb - they are usually sort of ovoid and often have two stalks coming up from the bulb - you want to cut the short part of the oval - each stalk will be on one half of the cut. take out the triangle center by holding the half upright (so that the bottom of the bulb is on the cutting board) and make a cut down each side of the triangle (hmm, i probably should have taken a picture of this). then lay each half so that the cut middle is on the board and slice thinly - it will leave you with crescent-shaped slices. don't cut up the stalky part - it's tough and weird.
save the nice feathery leaves for garnish - pretty and tasty!
for the orange, cut off the top and bottom and then set it on a cutting board and with a sharp knife, cut the skin and white pith from the flesh in thin strips - basically, you don't want any of the pith still on the flesh, because it is ugly and bitter. it's fine if there is some of the orange on what you cut away, because you can squeeze it over the fennel to add some acid and flavor.
turn the orange on its side and cut thin slices (or thick, i suppose. i prefer thin).
you are almost done!
toss the fennel with the orange juice you can squeeze from the peel and some lemon juice to taste. pile it on a plate. then place the oranges around in a pleasing fashion and drizzle it all with some good olive oil. if you happen to have one of those fancy olive oils with orange flavoring, now is the time to use it. sprinkle with salt - kosher is fine, or something fancy like fleur de sel - and freshly ground black pepper.
top the whole beautiful mess with some oil-cured black olives. they are usually found in the grocery store's olive bar and are somewhat chewy and very rich and delicious.
other possible additions to this salad could be toasted nuts or some goat cheese, but it is very nice and fresh as it is. also, you don't have to use blood oranges, but they sure are pretty.