Zurich Airport: Take Swiss Federal Railways trains to Visp (usually direct or with one easy change in Zürich), then the half-hourly PostBus to Saas-Fee. Allow roughly 3–3¼ hours total: about 2¼ hours to Visp plus a 50-minute bus ride and connection time. A full-fare point-to-point journey is roughly CHF 90–110; Swiss Travel Pass or Half Fare discounts can change that materially. Do not rent a car just for this transfer—you will park it at the edge of Saas-Fee.
Geneva Airport: Take the train to Visp—often direct, otherwise one change—then the PostBus to Saas-Fee. Realistic total is about 3¼–3¾ hours, depending on the connection; budget roughly CHF 85–105 full fare. It is a long but straightforward rail-and-bus journey, not an airport-shuttle destination.
Visp railway station: This is the practical rail gateway. Take the half-hourly PostBus to Saas-Fee; the ride is about 50 minutes and the terminal is central. Buy through to Saas-Fee with your rail ticket or from the driver. On Friday evenings, ski-changeover periods and snowy days, take an earlier bus if you have a fixed connection—extra buses may run, but you may still stand.
Brig railway station: Brig is useful if your long-distance or EC train stops there rather than Visp. Continue toward Visp and take the Saas-Fee PostBus, or use the relevant onward bus connection; allow about 1¼–1½ hours to Saas-Fee in normal conditions. In practice, check the SBB journey planner and buy one through ticket rather than improvising separate legs.