To understand how best to get to Leukerbad, you should study the map of the area in detail. In general, it's quite easy to do, as the village is considered a very popular vacation spot not only for international tourists, but also for locals.
The ski resort of Leukerbad is a three-hour drive from Geneva airport. Once there, your best bet is to take an Inter Reggio train ticket to Leuk. The journey will take you about 2.5 hours. You will then need to take a bus to Leukerbad, which runs every 30 minutes.
To find the most suitable route, you can check train timetables here: www.sbb.ch.
If you want to get from Geneva airport to the snowy resort by car, take the A1 to Lausanne and then turn onto the A9/E62. After about an hour you will see a sign Leukerbad, Leuk-Stadt. After that you will have to drive along the serpentine for about 15 minutes and you will reach the end point of the route.