Traveling in Switzerland is an absolute delight. The trains and post buses are timely & efficient and booking tickets online or at the (train/bus) stations is very easy. Many people who hike the Alpine Pass Route (APR) fly into Zurich and take a train to Sargans where you begin your trek or take a post bus to Weisstannen. If completing the trail in Montreaux, leaving out of Geneva is the best option.
Although the Alpine Pass Route is challenging there are many transportation options to/from destinations along the trail. The best method for trekkers and independent travelers are Postbuses & Trains, which are efficient, almost always on time, & safe/comfortable. However, for travelers taking several day trips and visiting lots of towns & villages renting a car is a better option. Be careful of speed trap cameras notorious in Switzerland and many parts of Europe as if you do not abide by the signed speed limit, you may have several speeding tickets waiting for you when you get home. Doing research and knowing the best method of transportation (train/postbus) can save you time. Trains and post buses are quite frequent in many towns but knowing the schedule, especially on Sundays, when transportation is less frequent will help you avoid missing your ride. I have listed bus/train options for each stage however the following links are helpful in determining to/from transportation destinations and options in Switzerland regarding land/air travel. You can book many tickets well ahead of time and get a sense of bus & train costs:
Train & Bus: