If you come by plane, the easiest way is to fly to Zürich international airport, take a train from there and then change to a bus in Sargans. When coming from Zürich airport by train, you have to change at Zürich main trainstation to the train travelling to Sargans. Other option is to take train to Buchs, which is another city right next to the boarder of Liechtenstein and Switzerland, but then train has to be changed once more so the best way is to travel to Sargans.
Outside the Sargans bahnhof there is a bus stop and the bus number 12 goes to Liechtenstein. It costs around 2,7fr for a student and 7fr for an adult.
Other airport near Liechtestein is Friedrichshafen in Germany which quite small and a bit nearer than Zürich but it's more difficult to find flights there as well as connecting tranportation to Liechtenstein.
If you are up for some budget travelling, Memmingen airport is appr. 150km away from Liechtenstein and Ryanair flies there from many destinations. From the airport there is a shuttle bus to the railwaystation (2,5€ one way) and a train to Feldkirch (see more information about how to get further from Feldkirch below) costs 32€ normal price and 21€ with Austrian vorteilscard.
There are no long-distance trains stopping in Liechtenstein but there are three main train stations just next to the boarder of it. Feldkirch train station is on the Austrian side, Buchs and Sargans in Switzerland. Right outside any of these stations bus stops from where you can take Liechtensteinian bus to travel anywhere you need to go in Liechtenstein.
Buses from Feldkirch to Liechtenstein are numbers 13 and 14, from Buchs to Liechtenstein are number 12 and 13, and from Sargans to Liechtenstein is number 12. Bus tickets cost normally around 7fr/adult and 2,7fr/student. Inside the buses there is always a screen, which shows the name of following bus stops, which makes it easy to know where to get off even if you hadn't been earlier in Liechtenstein.
It's easy to drive to Liechtenstein from any direction. Roads are generally in a good condition and traffic is not aggressive at all. Drivers are usually very polite and give enough space to other drivers as well as to pedestrians.
More posts will be coming soon so stay tuned, and in case you have questions, feel free to ask in the questions section.