The perfect buttercream is an illusive goal. Several key factors are involved in creating an excellent butter cream.
1. The butter. You need to make sure you butter is at room temperature. Always use unsalted butter. I usually buy the generic HEB brand in Texas for $1.99/4 sticks.
2. The sugar. Powdered, and most importantly sifted. Don't buy a stupid metal sifter that you have to fuss with the handle. It's too slow going. I prefer to use a mesh strainer and bang my hand on the edge. Whatever doesn't fall through the sieve, do not reuse or crush or force through the mesh. Toss it. Those little bits are the arch enemy of frostings: lumps.
3. The ratio of butter to sugar. Tricky. Depends on what you like, sweeter or buttery-er. I prefer a less sweat buttercream. Thus my ratio is 1 stick of butter 2 cups powdered sugar. You can of course adjust to your own preferences. If you do this in small increments, you can experiment quite a bit to make sure you have the ratio to your preferences. Add the sugar slowly after you hit 1 1/2 cups. Perhaps in quarter cup increments until you get the consistency you want.
4. The extras. I like to mix in pure vanilla extract (get it at Costco it's cheap and great quality). At least 1 teaspoon. Sometimes, up to a tablespoon. Again, add in small increments and taste a lot. You will find your perfect buttercream. You can also try various other extracts such as raspberry, almond, lemon, orange...all in small increments until you get the desired flavoring.
5. The milk. Depending on what's around the house, I prefer to use half and half as the 'milk' of the buttercream. Add a tablespoon at a time to control the consistency. You can always add more, you can't take milk out. If you dump in too much milk then the consistency is off and crappy, so you add more sugar, which then needs more butter....no bueno. You can use heavy cream or you can use nonfat milk if you are insane. All should be at near room temperature. You don't want your ingredients at all different temperatures, causes freaky deaky things to happen.
Now that we have covered all the ingredients, you have two mixing options: a stand mixer or a hand mixer. I've used both. It doesn't matter, just use what you have already. Mix the butter by itself first. Less than a minute of mixing. Add in the sugar (2 cups sifted), the vanilla or other flavoring, and 2 tablespoons of milk or cream. Beat. Check flavor and adjust accordingly with sugar and milk or cream.
I like to frost immediately, but frosting cupcakes is often just a nuisance to me. I am not a master decorator and I have never noticed anyone complaining about my cupcakes because they are not masterful works of art. Spoon on about 2-3 tablespoons of frosting in the center and you can use a knife, a spoon, or some fancy utensil.
If you like to pipe frosting on, I like to chill my frosting in the fridge for about a half hour before frosting. I like the control of the frosting better that way.
Buttercream can be colored with simple food coloring. Buttercream can be saved in the fridge for about a week. Buttercream can also be 'cut' with cream cheese. If you substitute half the butter for cream cheese, you will have an entirely different frosting, which is an excellent substitute when you want to mix it up.