One of the questions I've been asked most recently at my stall is how I get my toppings so smooth/firm/nice (thank you to everyone who has been so complimentary). I don't know that I have any special secrets but this is what I do to make and apply a tasty buttercream.
First, butter - it must be soft and smooth. I chop mine up a bit and put in the microwave on high for 20-40 seconds depending on whether it has been out in the kitchen or on the fridge. I usually make basic buttercream packet of butter at a time! You probably want to be a bit more economical - I think you'll need 150g for 12 cupcakes. Beat the butter until it is smooth and roughly the consistency of mayonnaise or Hollandaise sauce (mmmm, eggs benedict).
Second, icing sugar. Sift it into your butter. Don't think you can get away with putting it in a bit lumpy (ok, you can sometimes, but it's not worth it). If you hate sifting, you can put your sugar in a large bowl and beat it with a balloon whisk to break it up and add air. An observation, the larger quantities in which you buy it, the less 'lumpy' it appears to be - when I have 3kg bags it will need very little sifting, but the sugar is always well compacted in a 500g box. Tip 1: Add it a little at a time to minimize icing sugar fog in your kitchen. Tip 2: You'll need twice as much as you think.
Third, blending. Your sugar can be mixed with your butter with a wooden spoon or with a hand blender, but when it starts to get stiff go easy on your hand blender (I broke my cheap one mixing buttercream, although it was a good excuse to my beautiful Dualit blender: see 27th October). Keep adding sugar until the mixture stands away from the bowl (in a dough like lump) when you add a new batch of sugar; it should soften back down and you may need to add a bit more sugar. When ready it should not drop easily from a spoon, but be soft enough to drop off when you flick the spoon or tap on the side of your bowl.
Fourth, flavour. Plain buttercream may be just what you need - subtle with vanilla and a great topping for carrot cake. If you're a novice stick to some easy to mix flavourings. Lemon juice is often suggested for a beginners lemon cupcake but, actually, the buttercream can split if you add too much. Better to start with an oil or essence - orange extract, vanilla extract or rose water will mix in easily. Add to taste and add more sugar if necessary to get back to your desired consistency.
Finally, application. Get the right kit. I use large plastic star nozzles in 7 or 8 point stars (large 7 is used on Toffee Apple for example). Apparantly there is no consistent numbering system for nozzles, so to give you an idea the nozzles are about 2 inches high with openings 1/4, 1/2 and 3/4 of an inch across. I prefer 30-40cm nylon or disposable bags (cheap disposable ones WILL split), any smaller and you have to refill more times, increasing the liklihood of air bubbles.
Once you have filled your piping bag (probably half full is enough to handle easily), twist the top to contain and put pressure on your icing. Swirl away in whatever pattern you like, twisting the bag slightly between each cake to maintain a consisten pressure.
Oh, and then add sparkles, sprinkles, drages, cherries, smarties, flowers, hundreds and thousands, chocolate shavings....