Would I travel by boat, or was enough road infrastructure in place in the middle ages to allow me to travel across mainland Europe? What cities and countries would I find myself passing through along the journey? It seems like a very long trip even by modern standards and I'd like to know more about how it was completed.
Can't answer everything in detail, but a common course for a Scandinavian would have involved a land journey that would have gone through the lands of the Kievan Rus, and then probably a naval route via the Black Sea. This would be due to the relative acceptance of these travelers in their lands (often Scandinavians formed a solid portion of the military positions in the region) and also the close ties and frequent trading between the Kievan Rus and Byzantines that would have made transit between the two regions very easy. For that matter, Scandinavia and Russia are not that far apart either so that can't be forgotten as a reason.
Source: A History of Russia and the Soviet Union MacKenzie and Curran