For those flying in from overseas..
Milan Malpensa Airport. Milan's international airport will be the best place to fly into if travelling from outside of Europe. You can spend a few days adjusting to the time zone, whilst taking in everything this metropolitan city has to offer - Leonardo da Vinci, pasta and gelato.
Once acclimatised, there's a fast train (Trenitalia InterCity) that can take you out to the coast. The route will be Milano Centrale to Santa Margherita Ligure-Portofino. We recommend upgrading classes for extra space, since you will likely be travelling with luggage. The main cabin will be busy in the summer.
For those flying in from Europe / U.K..
The fastest way to get from London to Portofino is to fly into Genoa. Sadly, there are only Ryanair flights (once or twice daily) from London Stansted Airport. From the main train station, you can take a train or taxi to Santa Margherita Ligure-Portofino.
Another method is to fly into Pisa (British Airways, Ryanair and easyJet) but the train to Santa Margherita Ligure-Portofino is a lot longer.
Lastly, if you wanted to avoid budget airlines, flying ITA Airways or British Airways from London Heathrow or London City Airport to Milan Linate Airport is a good method. It only takes 20 minutes to get from Milan Linate Airport to Milano Centrale, after which you can take a train down the coast.