Ted Stevens Anchorage International Airport: Rent a car at ANC if you want Portage, Whittier, Turnagain Pass, or your own timetable: Girdwood is about 45–60 minutes south via the Seward Highway in clear conditions, longer in summer traffic or winter weather. If you are staying at Alyeska and not touring beyond the valley, pre-book an airport-to-Girdwood shared/private shuttle; it is the sensible car-free option, but expect roughly US$100+ each way rather than city-airport pricing. There is no useful walk-up public-airport transfer to rely on.
Anchorage Alaska Railroad Depot: In the summer rail season, the Alaska Railroad is the scenic, no-driving alternative from Anchorage to Girdwood; allow roughly 2½ hours and budget about US$100 or more one way depending on service and date. Reserve ahead, then arrange lodging pickup or a local shuttle from Girdwood’s stop—this is not a station in the middle of a dense town center.
Girdwood Airport / landing strip: Do not plan commercial arrival here. It is a short strip used principally by small prop aircraft and heli-ski operations, not a practical gateway for ordinary visitors.