The first time I had limoncello was in Italy. It was homemade by my wife's Italian relatives. It was a powerful but tasty "digestivo" that was served at the end of a meal. He gave me a bottle which survived the suitcase ride back to the States.
I decided to start with this recipe I found on the Food Network by Giada De Laurentiis.
The result was tasty but a little too sugary and not enough kick. So there are some lessons to be learned. But this first taste was right afterwards. The finished product should sit in a pantry for a few weeks to a month to let it mellow.
During the time that this first batch was steeping, I was doing some online research and noticed that other recipes called for 1 bottle of vodka and one bottle of everclear (or sometimes grappa). I am told that one can get pure alcohol in Europe. Which is probably what I tasted in Italy. I have seen jars of "moonshine" at BevMo so I may try that in version 2.0.
Steeping for 4-5 days is not enough. It should be two weeks to a month in a cool dark place. A few sites recommend using a large sun tea jar so that you can screw it shut.
Another thing was the fact that my limoncello was clear. The limoncello I remember was opaque. Now it is possible that with more steeping time the alcohol may begin to get opaque. This recipe (which is closer to what I'll try next time) says that adding the simple syrup while it's warm will make the mixture opaque.
This is a great site that clearly explains all of the steps.
Another excellent site with lots of explanations.
Lots of different ideas in the responses.
LA Times article.
Rick Steves article on the topic.
How to Serve
Keep the lemoncello in the freezer and serve straight up in a small glass after dinner.
You can add a little ice and club soda for a refreshing summer drink.
Here is a site with lots of drink recipes that include limoncello.
Or perhaps a limoncello collins.