Travel to Innsbruck
You can reach Innsbruck easily through its airport (http://www.innsbruck-airport.com/en/) which has direct flights from several major European cities (e.g., London, Amsterdam, Frankfurt, Vienna, etc.).
From the airport you can easily use public transportation: the bus line F stops right in front of the airport terminal and brings you directly to the city center. (More information is given on the webpage of the "Innsbrucker Verkehrsbetriebe" http://www.ivb.at/en/)
There are excellent train connections to and from Innsbruck, for example trains run several times per day directly from Munich to Innsbruck (duration is less than 2 hours) and from Vienna to Innsbruck (duration typically around 4 hours).
Upon arrival at the central railway station in Innsbruck ("Innsbruck Hauptbahnhof") you are in walking distance to the city center and have a variety of buses to continue your journey.
Via car you reach Innsbruck on the highway A12 "Inntalautobahn".
Important: Please note that parking in Innsbruck is expensive and unpaid parking spaces are nearly non-existent. If you plan to come by car, you will probably need to arrange for a parking space with your hotel (if possible) or use one of the city's public parking garages.
Public Transportation in Innsbruck
In the city center of Innsbruck you can reach most attractions on foot.
Innsbruck also offers the possibility to rent city bikes as it is possible now in many European cities. More information can be found here! (http://all-inn.at/sport-funsport-und-action-in-innsbruck-tirol/radverleih-rad-fahrrad-leihen-mieten/citybikes/)
There are plenty of buses that easily bring you through the city. (More information is given on the webpage of the "Innsbrucker Verkehrsbetriebe" http://www.ivb.at/en/).
A single ticket costs 2.30 EUR when purchased at one of the ticket machines at the bus stops and 2.70 EUR when purchased with the bus driver.
There are reduced prices for a weekly ticket (called "Wochen-Ticket") or if you buy a ticket for 5 separate rides on the buses (called "5-Fahrten-Ticket) as well as, e.g., for senior citizens and children.