your basic vanilla buttercream (not french or italian buttercream, which is a ton of work and unpredictable) is to beat two sticks softened butter until creamy, and then beat in powdered sugar to taste, generally, 1/2 lb powdered to 1/2 lb butter (two sticks). Add 1-2 tsp pure, real vanilla extract, a tiny pinch of salt if you didn't use salted butter (I always use salted butter... trust me, you want salt in it one way or another... otherwise it won't have balanced flavor), and beat until fluffy. If it is too thick, add a few drops of milk, but you shouldn't need to. This same recipe can be varied with other flavors - omit vanilla and add orange or lemon zest, other other flavored extracts like mint or almond, etc.
This is your basic real vanilla buttercream frosting and works well on everything. My advice: don't use shortening! Hyrdogrenated oils are really bad for you, are the main cause of heart disease, and have no flavor. Real butter is the way to go, baby.
If you want a lighter icing, you can just do Chantilly Creme (whipped cream) - whip cold, very fresh cream to soft peaks, add regular sugar and vanilla to taste (only a little of each) and beat to desired consistency. It is a lovely, light, vanilla frosting for delicate cakes. Be careful not to overbeat or you'll have butter instead
not sure what proportions since we just throw the stuff together. Either nuke it in the microwave or do in a saucepan. We add lots of vanilla extract! We use it on cakes, cinnamon rolls, cupcakes, etc!
Either way, leave the butter and cream cheese out on the counter until roomtemp, or nuke for just a few seconds to soften, but don't melt! Then cream together, then add other ingredients and beat until light & fluffy.