This is a frequently discussed question, so I thought it might be useful to create a thread to post in the top questions.
There are pros and cons for different transportation methods, and it's important you make an informed choice about what works for you.
Public transport in Switzerland is efficient, clean, punctual, environmentally friendly and often takes you through tremenous scenery. Villages, towns and cities are linked through an excellent integrated system (whereby bus timetables are often linked to train arrival times, so you can travel seamlessly). Buses and sometimes even trains or funiculars can take you up to high villages. There are some places that are not accessible by public transport, but this is a very very small percentage of the country.
Journeys can be planned from your start point (say in a big city or at the aiport) all the way to a tiny rural bus stop. The useful Swiss public transport website www.rail.ch or www.sbb.ch/en will help you work it all out. Simply enter your "from" point and your "to" point. You need not enter anything in the "via" box unless you have a particular route in mind. Where the website offers you a number of options for a town or village, this means that the place has a number of stations and bus stops. It will automatically default to the main one, and you can just choose that if you are unsure. The website will only offer transfers between trains and buses etc that are possible. For example, if it says there are 5 minutes between trains, this will be possible for a person walking at a standard pace. You can also check fares on the site.
There are a number of travel passes that can save you money:
Specific areas often have their own regional travel passes, some of which you pay for and some of which come free to those staying in hotels etc. Check the local websites, or discuss with the local tourist office for more information.
Many people travel without difficulty with their luggage on the train (in luggage areas at the end of the carriage or behind some seats). Some travellers feel reassured by having a thin wire type bike lock to secure their baggage, if they are going to be out of sight. It is also possible to arrange to have your baggage transported for you:
Many stations have secure lockers or left luggage offices for baggage, so it is possible to leave your bags and sight see en route.
Public transport is unfortunately not yet fully accessible across the network. However, with advance notice, assistance can be provided to those with mobility or sensory challenges:
Car driving/ car hire:
Driving in Switzerland is a good option for some people. Roads are well maintained and sign posted. For people who enjoy the classic motoring experience, there are some great mountain passes to take (largely Summer only). For those with mobility problems, fatigue or social/behavioural difficulties, vehicle hire may be very practical.
In the winter, driving is more challenging. Roads are quickly ploughed and salted, but it is important to plan ahead. Hire cars will usually come with winter tyres and chains in the boot (trunk). Those driving their own cars from other countries would be wise to have winter tyres and certainly must carry chains. It's a good idea to take a look at these before you need them, so that you don't get too stressed if that time comes. It's also useful to carry a blanket (a small silvered blanket from outdoor shops is an option), a torch with batteries, an ice scraper (usually provided with the hire car) and ideally some type of small shovel (a small plastic one can do). It is probable that you won't need to use any of these things, but it's good to be prepared. Generally speaking, driving in Switzerland is an ordinary every day activity without any difficulty.
Many people drive with their headlights on year round, and this is seen as sensible practise. If you speed, prepare for a large fine. Some may find that people drive quite close to each other's bumpers - try to keep your own distance and do not see this as an aggressive act. Slip roads on motorways are often quite short and people can drive onto the motorway quite quickly. Be prepared to move over.
If you plan to drive on any motorway in Switzerland (which is very likely), you will need to make sure your car/ hire car has a motorway vignette. This is a small sticker that goes on the windscreen. It costs CHF 40 and lasts for one year. There is no shorter duration version. Hire cars hired in Switzerland usually come with this already on the windscreen. If you drive on the motorway without this, you can be heavily fined. You can buy it at border crossings, petrol/gas stations across the country and near border crossings.
Parking in many cities and towns can be expensive and sometimes a bit hard to find. If this will be a problem for you, you may like to consider using public transport for the urban portions of your trip.
If you plan to pick up your car in one country and drop it off in another, check carefully about drop off fees. These are often very high. If this is the case for you, you might want to think about dropping off your hire car in the country you hired it in, and hiring another car in Switzerland. Or, you might want to think about public transport for Switzerland.
Cars do have an environmental impact that is important to think about. There are some lovely car free villages in Switzerland where you can really enjoy the fresh air. If these interest you, you will need to travel in by public transport (leaving your car in a car park). Some, such as Zermatt, offer electric taxis, so those with lots of luggage or mobility or fatigue problems need not be put off visiting.
Switzerland is covered in well marked hiking/walking paths. You might also want to bike, climb, ski and even snow shoe to your destination. Wherever you want to get to, there's a way!