The closest airport to Ascona is the Lugano Airport, about 40 minutes away by car.  This is a smaller airport, serving a few European carriers including Swiss Air and Flyaboo.  Car rentals are available at the airport and maps of the region are given out at all car rental agencies.  The drive from the airport to Ascona is fairly straightforward, but be sure that you meet all of Switzerland's driving requirements before driving there and that you have some idea of the route that you will be taking.  Most road and street signs are not in English. 

Should you choose not to drive to Ascona from the airport, there is also a shuttle bus available.  Bus service to and from the airport and Ascona is available seven days a week.  See the website for more information including prices.  Shuttle bus reservations can also be made via the site.

Traveling to Ascona by train is also quite simple.  The city is located on the International Railway Line and is accessible by rail from many major points throughout Europe.  See the link for more information.